BREAKING: Putting our rational skills on display!

SATURDAY, SEPTEMBER 29, 2018

Twilight of the animals: We rational animals are always quick to put our skills on display.

So it was in the case of Thursday's Senate hearing, which may have been scripted by Alice's queen:

"Hearing first, investigation later," we rationals said. And not only that:

"Let's put a time limit on our probe! We wouldn't want to take a chance on possibly learning too much!"

So we modern Americans play, in the twilight of our culture. Also this:

Within the framework of our rationality, Thursday, July 1, 1982 can't be scored as a weekend night. More specifically, it wouldn't have been the start of that year's July 4 weekend!

The Washington Post accepts this framework in this morning's otherwise instructive news report—a news report which makes us wonder if Kavanaugh's voluntarily provided calendars may turn out to be the equivalent of Nixon's undestroyed tapes. Featured in the Post's photograph is a familiar type of event—a liberal leader, Senator Whitehouse, arriving at the scene of the crime exactly one day late.

We mention Whitehouse for a reason. It's easy for us liberals to spot the dissembling in Kavanaugh's testimony—and it must be said that, for better or worse, Kavanaugh is an astoundingly unskilled dissembler.

The fact that he did a lot of dissembling doesn't necessarily mean that he assaulted Christine Blasey when she was 15. That said, his endless, amazingly unskilled dissembling cohabited on Thursday with a familiar phenomenon—the amazing incompetence put on display by our own tribal leaders.

First example:

Why did Senator Feinstein, and all the others, wait so long to deny the claim that she and/or her staff leaked the contents of Blasey Ford's confidential letter, thereby bringing Blasey Ford into the public eye?

Why in the world did they wait so long? We have no idea, but it amounted to (very familiar) intellectual misfeasance when the Democrats allowed this claim against Feinstein and her staff to go unchallenged so long.

If you want to inform yourselves farther, here is The Intercept's Ryan Grim saying that neither Feinstein nor her staff leaked the information in question to the Intercept, the site which produced the first public report concerning Blasey Ford's allegation.

Conservatives watching Thursday's hearing saw Feinstein fingered again and again before she finally got around to objecting. In these ways, our tribe's astounding incompetence contributes to false belief on the part of the other tribe's members.

Second example:

Anyone watching Thursday's hearing saw Kavanaugh claim, again and again, that everyone named by Blasey Ford had "refuted" her claim about the party or gathering in question. This was said again and again and again and again. As Kavanaugh kept repeating this claim, our tribal leaders performed like the famous "potted plants" of Watergate-era fame.

Our team has performed in such pitiful ways for at least three decades. It has been impossible to call liberal attention to this fact. In large part, this explains the way we got to the place where it falls to Donald J. Trump to make Supreme Court nominations.

In short, we created this amazingly stupid and dangerous world. The twilight of the rational animals achieved its full flower through us.

How else have we gotten to this place? If you watched Tucker Carlson on Monday night, you saw this appalling performance during his opening monologue:

CARLSON (9/25/18): There's a flip side to the new system. Because the accused are guilty by definition, the accuser suddenly have no responsibility to make credible claims. And we're seeing that principle in action too.

We covered the story all last week. Five nights in a row we said that we are giving Christine Ford every benefit of every doubt, and we did that. But let's be honest now. Not many of her claims would hold up in an actual court, the one governed by the justice system we thought we had until about 10 days ago...

When did this alleged assault take place? Ford can't say. When did it happen? She doesn't know. Where are the witnesses to this? Well, there aren't any. The few people Ford has named deny it happened. When was this first reported to authorities? Well, it never really was.

The story came out in stages. It was a recovered memory, apparently summoned by a psychotherapist 30 years after the fact. And even then, it was another six years before Ford named Brett Kavanaugh specifically, at exactly the point he was being nominated for the Supreme Court.

That's not our analysis of the case. It's the position of Ford's lawyers, nearly all of whom double as Democratic Party activists and operatives and some of whom defended Bill Clinton from far graver sexual assault claims when he was accused.

That doesn't mean Ford is lying. But it does raise legitimate questions so does a lot of her behavior.

Carlson made the same false claim about the people Blasey Ford named.

"The few people Ford has named deny [the alleged assault] happened?" In fact, one of the people Blasey Ford named has said she believes it did happen. (Two of the people she named are said to have perpetrated the assault.)

That was penny-=ante stuff; we also note the apparent false claim about when Blasey Ford first named Kavanaugh as her alleged assailant. From there, Carlson went on to other false claims, including the claim we've highlighted.

Question:

When have Blasey Ford's lawyers ever said that her allegation is the result of a "recovered memory?" We find evidence of no such assertion, nor did Carlson specify any such statement.

That said, he was soon repeating this claim, several times, in the face of a less than fully competent liberal guest. As he did, he said that such "recovered memories" are less reliable than the regular kind.

In a familiar pattern on Carlson's show, his eager but overmatched liberal guest failed to challenge his bogus assertion. Several million viewers thus became even more misinformed, in a familiar old way.

At least sine the rise of Rush Limbaugh in the 1980s, such acts of disinformation have ruled American discourse. When these acts have come from the right, the liberal world has typically slumbered and slept and dozed and scratched and dreamily chosen to burble. Either that or we've gone on Carlson's show, where we typically offer the silence of the sacrificial lambs.

Not all the acts of disinformation have come from the right. During the Clinton/Gore/Clinton years, many of these acts came from the upper-end mainstream press, the source of employment to the many people who pose as our tribe's liberal leaders.

Our leaders have tended to stare into space as dis- and misinformation have come to rule our discourse. On the rare occasions where we manage to show up at all, we tend to show up one day late, as Whitehouse did yesterday morning.

People like Carlson can say what they please. Beyond that, attacks on the Clintons—including misogynistic attacks on Hillary Clinton—will run all over the New York Times without a word from our leaders.

(Those misogynistic attacks ran on cable for decades. Our liberal leaders clamored to get on the programs in question, so they could play right along.)

We reaped the whirlwind of our endless silence when Donald J. Trump drew an inside straight and squeezed his way into the White House. So it has gone in the never-ending twilight of the rationals.

There's no way to cover the full extent of this moral and intellectual breakdown, but our own tribe's relentless failure is a very large part of this mess. We're in this twilight up to our necks—this twilight of the rational animals, which could sweep us all away.

Is Blasey Ford's allegation true? We can't tell you that. But on Thursday morning, she rose to perform her citizen's duty. Over here in our self-impressed liberal tents, we rise to that level quite rarely.

Hearing first, investigation later! And don't let the probe run too long!

In fairness: After performing his acts of disinformation, Carlson typically spends some time airing tape of low-grade, inane behavior by our own liberal players.

These parts of Carlson's show are often all too instructive. If you ever watch his show, we're afraid you might see what we mean.

In these ways, the other tribe learns that we liberals can't be trusted. All too often, viewers see Carlson making a decent point.

THE GUARDIANS FILE: What you saw at yesterday's hearing!

FRIDAY, SEPTEMBER 28. 2018

Plato saw the same thing: "It's not that easy being green," Kermit the Frog has said.

"People tend to pass you over 'cause you're not standing out like flashy sparkles in the water." Or at least, so Kermit has claimed.

Was Kermit feeling sorry for himself, or did he have a strong point? We'll leave that to the historians! But at least within our failing society, it's also "not that easy" to cast oneself in the guardian's role—to play the role within our society which Plato prescribed long ago.

Years ago, sacred Plato said a just city would need leadership from a guardian class. Indeed, he said a just city might need to be ruled by such an elite.

According to Professor Lane, Plato's Socrates said these "guardians"—these "philosopher kings" and "philosopher queens"—would have to live simply and communally. They would have to be educated in certain ways. They would have to be "dedicated to what is good for the city rather than for themselves."

They'd also have to be philosophers! Or so Plato said!

Just this once, let's be clear! Plato lived at a different time—at "the dawn of the west." When he was voicing these prescriptions through the person of Socrates, he was discussing the way to create a "just city."

He wasn't discussing the needs of a large continental nation like our own failing state.

It's estimated that Plato was born between 429 BC and 423 BC—that is, during the fifth century BC. The bulk of his adult life was therefore lived during the fourth century BC.

How large was the Athens of this day? You're asking a significant question. The leading authority on this matter offers this overview:

Estimates of the population of ancient Athens vary. During the 4th century BC, there might well have been some 250,000–300,000 people in Attica. Citizen families could have amounted to 100,000 people and out of these some 30,000 would have been the adult male citizens entitled to vote in the assembly. In the mid-5th century the number of adult male citizens was perhaps as high as 60,000, but this number fell precipitously during the Peloponnesian War...From a modern perspective these figures may seem small, but among Greek city-states Athens was huge: most of the thousand or so Greek cities could only muster 1000–1500 adult male citizens each; and Corinth, a major power, had at most 15,000.

The non-citizen component of the population was made up of resident foreigners (metics) and slaves, with the latter perhaps somewhat more numerous.

When Plato imagined the structure of a "just city," he was discussing the needs of a city-state of this general size.

Plato held that this Athens should be ruled by the philosopher kings and philosopher queens who constituted the guardian class. In the modern context, one would more simply hope that various individuals and groups would step forward to play the role of the guardian, offering such expertise as may serve the public interest.

It isn't that easy being green? Given the nature of our mass society—given the situation experts are calling "the twilight of the rational animals"—it's virtually impossible to serve in the guardian role within our broken mass culture. Over the past thirty years, we've seen quite a few who have tried and failed:

We think of several efforts by Paul Krugman, including his attempt to encourage the mainstream and corporate liberal press to describe Paul Ryan as he actually is. Try and try though Krugman did, he couldn't get others to follow his lead, not even corporate liberals.

(It's an established part of Hard Pundit Law. There will always be a Judge Starr, a Ryan or a Comey who is being universally hailed as the nation's most upright person. Few Dems need apply.)

We think of Kevin Drum's attempt to present basic information about the recent history of lead exposure. Drum's attempts to spread information ran headfirst into the demagoguery of corporate clowns like Rachel Maddow, who used her high corporate platform to dumb the liberal world down as she kept selling the car.

We think, of course, of Gene Lyons' 1995 book, Fools for Scandal: How the Media Invented Whitewater, which began as a full-length report in Harper's. Alas! By "the media," Lyons principally meant the Washington Post and the New York Times. For this reason, his reporting on the early years of the war which eventually sent Donald Trump to the White House was disappeared by the various corporate players we liberals foolishly think of as our tribal leaders.

We think of our own endless work of the so-called "war against Gore," the twenty-month journalistic scam which sent George W. Bush to the White House.

As with Whitewater, so too here. This ugly, stupid war was largely conducted within the mainstream press by leading "liberal" figures. For this reason, our own attempts to serve in the guardian role were destined to be disappeared by the various mainstream careerists who pose as liberal titans.

We also think of the way the mainstream press reports domestic and international public school test scores. Returning to attempts by Krugman, we think of the way the mainstream press disappears the basic data concerning health care spending in the United States, which amounts to an astonishing form of looting.
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For reasons which go unexplored/unexplained, it has been impossible to get the mainstream press to perform its normal duties with respect to such basic pieces of information. Those who try to play the guardian role with respect to such topics are destined to learn a basic sociological fact:

Performing this role in our mass corporate culture is, in the end, considerably harder even than being a frog!

In all these areas, "corporate liberal" speak-chuckers have reliably served the interests of corporate ruling interests. (Chomsky describes this process as "manufactured consent.") Meanwhile, make no mistake:

You've seen similar patterns in recent weeks concerning the liberal world's hapless attempts to address the nomination of Brett Kavanaugh to the Supreme Court.

In our next report from the guardians file, we'll take a brief look at Professor Wilentz's recent attempt to play the guardian role in this matter. For today, let's understand what you saw at yesterday's televised hearing.

Citizens, please! Yesterday's hearing was the latest iteration of a pattern as old as so-called humankind.

Yesterday's hearing can be viewed in more than one way, of course. Depending on which corporate channel you were being propagandized by, you were encouraged to react to the testimony in substantially different ways.

There are various ways to understand yesterday's hearing. But for those who principally saw a power elite rushing through a major power grab, we'll only say that yesterday's hearing was an echo of human experience during the age in which Plato lived.

Yesterday's hearing was the latest replay of familiar events from that earlier age. The leading authority on that era has thumbnailed the matter as shown below:

Before the first attempt at democratic government, Athens was ruled by a series of archons or chief magistrates, and the Areopagus, made up of ex-archons. The members of these institutions were generally aristocrats, who ruled the polis for their own advantage. In 621 BC Draco codified a set of "notoriously harsh" laws that were "a clear expression of the power of the aristocracy over everybody else." This did not stop the aristocratic families feuding amongst themselves to obtain as much power as possible.

Therefore, by the 6th century BC, the majority of Athenians "had been 'enslaved' to the rich", and they called upon Plato's ancestor Solon, premier archon at the time, to liberate them and halt the feuding of the aristocracy. However, the "enfranchisement of the local laboring classes was succeeded by the development of chattel slavery, the enslavement of, in large part, foreigners."

Solon, the mediator, reshaped the city "by absorbing the traditional aristocracy in a definition of citizenship which allotted a political function to every free resident of Attica. Athenians were not slaves but citizens, with the right, at the very least, to participate in the meetings of the assembly." Under these reforms, the position of archon "was opened to all with certain property qualifications, and a Boule, a rival council of 400, was set up. The Areopagus, nevertheless, retained 'guardianship of the laws'"...

Not long afterwards, the nascent democracy was overthrown by the tyrant Peisistratos, but was reinstated after the expulsion of his son, Hippias, in 510. This sort of aristocratic takeover "was ended by the appeal by one contender, Cleisthenes, for the support of the populace." The reforms of Cleisthenes in 508/7 undermined the domination of the aristocratic families and connected every Athenian to the city's rule. "Cleisthenes fixed the boundaries of the polis as a political rather than a geographical entity—boundaries which Solon had left permeable—by formally identifying the free inhabitants of Attica at that time as Athenian citizens." He did this by making the traditional tribes politically irrelevant and instituting ten new tribes...

A third set of reforms was instigated by Ephialtes in 462/1. While his opponents were away attempting to assist the Spartans, Ephialtes persuaded the Assembly to reduce the powers of the Areopagus: "in effect stripping it of all its controlling and supervisory powers and leaving it only as a court for cases of homicide and certain offences of sacrilege." At the same time or soon afterwards, the membership of the Areopagus was extended to the lower level of the propertied citizenship.

In the wake of Athens' disastrous defeat in the Sicilian campaign in 413 BCE, a group of citizens took steps to limit the radical democracy they thought was leading the city to ruin. Their efforts, initially conducted through constitutional channels, culminated in the establishment of an oligarchy, the Council of 400, in the Athenian coup of 411 BCE. The oligarchy endured for only four months before it was replaced by a more democratic government. Democratic regimes governed until Athens surrendered to Sparta in 404 BCE, when government was placed in the hands of the so-called Thirty Tyrants, pro-Spartan oligarchs. After a year pro-democracy elements regained control, and democratic forms persisted until the Macedonian army of Phillip II conquered Athens in 338 BC.

There's a lot to ponder there. Still, viewers of yesterday's hearing might consider the possibility that they were watching a TV rerun, in which they saw human history being relived. Consider:

"In the wake of Athens' disastrous defeat in the Sicilian campaign in 413 BCE, a group of citizens took steps to limit the radical democracy they thought was leading the city to ruin. Their efforts, initially conducted through constitutional channels, culminated in the establishment of an oligarchy."

The establishment of an oligarchy! Especially in a mass society, citizens opposed to this type of human impulse are badly in need of the services of a capable "guardian class." They must hope that this class won't be undermined by the work of hidden corporate elites and their endless enablers.

A final note for today. In his famous Seventh Letter, Plato recorded his reaction to the ascension to power of "the so-called Thirty Tyrants." In this translation, we think Professor Lee has it just about right:

PLATO: The existing constitution, which was subject to widespread criticism, was overthrown...and a committee of Thirty given supreme power. As it happened some of them were friends and relations of mine and they at once invited me to join them, as if it were the natural thing for me to do. My feelings were what were to be expected in a young man: I thought they were going to reform society and rule justly, and so I watched their proceedings with deep interest. I found that they soon made the earlier regime look like a golden age. Among other things they tried to incriminate my old friend Socrates, whom I should not hesitate to call the most upright man then living, by sending him, with others, to arrest a fellow-citizen, and bring him forcibly to execution; Socrates refused, and risked everything rather than make himself a party to their wickedness. When I saw all this, and other things as bad, I was disgusted and withdrew from the wickedness of the times.

The democracy was soon restored, but Socrates was brought to trial on “a monstrous charge.” His subsequent execution finished off Plato as well:

“The more closely I studied the politicians and the laws and customs of the day, and the older I grew, the more difficult it seemed to me to govern rightly,” he said in the Seventh Letter. “Nothing could be done without trustworthy friends and supporters; and these were difficult to come by in an age which had abandoned its traditional moral code but found it impossibly hard to create a new one.”

Plato abandoned his thoughts of a political career, deciding to spend his time dreaming up the perfect republic. Yesterday, we Americans saw a version of these events on our giant screens.

“Nothing could be done without trustworthy friends and supporters, and these were difficult to come by," Plato thoughtfully said. For "trustworthy," we'd substitute "capable"—and we'd say that he was seeking the intercession of a guardian class.

Our corporate liberal pseudo-guardians have been undermining progressive interests for at least thirty years. In our next report from the guardians file, we'll consider the recent attempt of Professor Wilentz to serve in the guardian role with respect to Kavanaugh's nomination.

Also, we'll raise the question we'll be pursuing for the next several months:

Let's consider the sweep of modern history, dating back to Lord Russell's work in 1901. Where have our logicians been during that expanse of time? More generally, through what means did our "philosophers" (our philosophy professors) decide to abandon their posts?

Tomorrow: The oligarchs' most recent rise

THE GUARDIANS FILE: No fish today!

THURSDAY, SEPTEMBER 27, 2018

We're watching the hearings instead: Was Christine Blasey Ford a credible witness? If so, does that mean that her account is accurate?

We're inclined to think her account is accurate. Does that mean her account is true?

Today only, we're assessing these age-old questions, as considered on cable TV. For that reason, we'll have no fish today. Our reports from the guardians file will resume tomorrow.

THE GUARDIANS FILE: Plato actually gets it right!

WEDNESDAY, SEPTEMBER 26, 2018

Our "philosophers" get it bad wrong: Sacred greats though they may have been, Plato and Aristotle did, in fact, get quite a few things wrong.

You can't exactly fault them for this. Each fellow held forth "at the dawn of the west." For that reason, they didn't have oodles of prior scholarship to draw on.

That said, when Aristotle turned to basic physics, he made at least several mistakes. As we've noted in the past, the leading authority on his work spells it out like this:

In his On Generation and Corruption, Aristotle related each of the four elements proposed earlier by Empedocles, Earth, Water, Air, and Fire, to two of the four sensible qualities, hot, cold, wet, and dry. In the Empedoclean scheme, all matter was made of the four elements, in differing proportions. Aristotle's scheme added the heavenly Aether, the divine substance of the heavenly spheres, stars and planets.

The basic four, plus the heavenly Aether? The majority of modern physicists will say that this looks to be wrong.

In a somewhat similar vein, it's somewhat comical to see a brilliant mathematician like G. H. Hardy offer a statement like the one posted below. Hardy offered this assessment in his iconic 1940 essay, A Mathematician's Apology, which is still in print:

HARDY (1940): I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply our notes of our observations. This view has been held, in one form or another, by many philosophers of high reputation from Plato onwards, and I shall use the language which is natural to a man who holds it.

Alas! When it came to "mathematical reality," Plato believed in something resembling our own modern-day "flying spaghetti monsters."

Have "other philosophers of high reputation" believed in much the same thing? Sadly, possibly yes. Meanwhile, Jim Holt, summarizing Rebecca Goldstein, tells us that many mathematicians believe in these mystical flying forms, as we'll remind you below.

Through no particular fault of his own, Plato advanced all kinds of claims which are hard to make sense of today. In at least one area, though, he rather plainly got it right. According to Plato, the healthy community—the sacred polis—needs the help, perhaps even the rule, of a well-trained guardian class.

What the Sam Hill is a guardian class? Given the way our modern-day guardians have tended to walk away from their posts, it's only natural that you might feel the need to be refreshed on this point.

Luckily, Encyclopedia Brittanica asked Princeton professor Melissa Lane to discuss this foundational concept. We'll start with this part of her essay, which appears under the title "Philosopher king:"

LANE: In Plato's Republic the leading character, Socrates, proposes the design of an ideal city as a model for how to order the individual soul. Such a just city will require specialized military “guards,” divided subsequently into two groups—rulers who will be “guards” in the sense of guardians, dedicated to what is good for the city rather than for themselves, and soldiers who will be their “auxiliaries.” Already at this stage of the Republic it is stressed that the guardians must be virtuous and selfless, living simply and communally as do soldiers in their camps, and Socrates proposes that even wives and children should be in common.

Lane's submission appears under the title "Philosopher king." She defines this as the "idea according to which the best form of government is that in which philosophers rule."

The form of government in which philosophers rule? Taken literally, that almost surely isn't the best form of government, though we'll never find out here, given the way our nation's "philosophers" walked away from their posts.

In Lane's treatment, Plato said the ideal city would have to have a soldier class. But above that group, the ideal city will need "guardians"—rulers who will be "dedicated to what is good for the city rather than for themselves."

As Lane continues, we reach the key point in her discussion. In Plato's mind, these "guardians"—these philosopher kings and philosopher queens—must in fact be philosophers, whatever that might mean:

LANE (continuing directly): At the outset of Book V, Socrates is challenged by his interlocutors to explain this last proposal. In response, Socrates expounds three controversial claims, which he acknowledges will expose him to ridicule. The first is that the guardians should include qualified women as well as men; thus, the group that will become known as “philosopher kings” will also include “philosopher queens.” The second claim is that these ruling men and women should mate and reproduce on the city’s orders, raising their children communally to consider all guardians as parents rather than attach themselves to a private family household. Those children, together with those of the artisan class, will be tested, and only the most virtuous and capable will become rulers. Thus, the group to become known as “philosopher kings” will be reproduced by merit rather than simply by birth. Finally, Socrates declares that these rulers must in fact be philosophers:

A society's rulers—its "guardians"—must in fact be philosophers? As she continues, Lane provides the specific statement where Plato's Socrates expresses this key point:

LANE (continuing directly): "Until philosophers rule as kings or those who are now called kings and leading men genuinely and adequately philosophize, that is, until political power and philosophy entirely coincide...cities will have no rest from evils...there can be no happiness, either public or private, in any other city."

"Socrates predicts that this claim will elicit even more ridicule and contempt from his Athenian contemporaries than will equality for women rulers or communality of sex and children," Lane says as she continues. "Many Athenians saw philosophers as perpetual adolescents, skulking in corners and muttering about the meaning of life, rather than taking an adult part in the battle for power and success in the city."

There you have it! According to Plato's Socrates, "political power and philosophy [must] entirely coincide." The pitfall to his proposal was this: "Many Athenians saw philosophers as perpetual adolescents, refusing to take an adult part in the battle for power and success in the city."

That's what many Athenians thought, back at the dawn of the west. As we survey our own failing society, we'd have to say that, allowing for a few adjustments, those "many Athenians" may have gotten it right!

In our badly floundering, failing society, the philosophy departments of our colleges and universities are clogged with logicians and ethicists, along with practitioners of other specific types. But alas! Despite our desperate need for their services, these people have long ago abandoned their guardian posts.

As we've looked at our failing culture over the course of the past many years, we've seen a crying need for the assistance of a class of logicians.

According to eighth-grade civics texts, our journalists are expected to provide such services. But as you know if you've ever watched a prime time "cable news" program, our highest-paid, most visible journalists often stumble over themselves as they work on the metaphorical level of 2 + 2.

Good God! Tomorrow, we'll ponder a few recent examples of the work our journalists provide. But as we the people beg the gods to give us the boon of a cogent discourse, our greatest logicians never intercede in these destructive gong shows.

They've walked away from their guardian posts! They spend their time, quite literally, on questions involving the "logic" of 2 + 2:

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.

What makes a proposition like 2 + 2 = 4 true? Our greatest logician since Aristotle devoted his time to such puzzles! To all intents and purposes, this nonsensical situation still obtains today.

Our logicians and ethicists, theoretical guardians all, have long ago walked off their posts. The lunacies of our failing discourse continue apace, night after night, absent any intercession from this lapsed guardian class.

Did you see Tucker Carlson on Monday night? Did you catch Hallie Jackson the following morning? Have you seen players from each of our tribes fervently saying Who They Believe in our current attempt at debate?

We're badly in need of the help of a guardian class. But our journalists are unable to serve, and our society's "philosophers" have largely walked away from their posts.

This pattern has given us President Trump. Neither of our warring tribes seems able to deal with this fact.

Tomorrow: Tucker Carlson, right and wrong, as "rational animals" flounder

THE GUARDIANS FILE: Major professors abandon their posts!

TUESDAY, SEPTEMBER 25, 2018

Semantics and paraphrase: Once upon a time, more than twenty years ago, it began to occur to us that our society's guardians had perhaps abandoned their posts.

The great, dark trees of incoherence cast a deep shade all around. As far as a person could see in the course of a day, or even in the course of a week, there was nothing but incomprehension. It was incompetence and inanity pretty much all the way down.

There was no Fox News at this time. There was no MSNBC. Within the big woods of "cable news," there was only CNN—CNN, and the rational animals who made their livings reciting script upon its various programs.

What made us start to think that the guardians had abandoned their posts? We think first of the great Medicare non-discussion of 1995 and 1996.

Every night, pundits would gather on CNN to pretend to debate the Republican Party's Medicare proposal. This proposal was being advanced by the new House speaker, Newt Gingrich.

Night after night, month after month, the discussion which wasn't a discussion would break down along mandated line—on Crossfire, let's say:

On Crossfire, the two disputants "from the left" would say that Gingrich had proposed cutting $270 billion from the Medicare program.

The two disputants "from the right" would say that no one was cutting the Medicare program at all. According to these disputants, the GOP plan had merely proposed "slowing the rate at which the Medicare program would grow."

Eventually, Republicans began to claim it was demagogic to use the term "Medicare cuts" at all. They began insisting that journalistic use of this term was the latest example of "liberal bias."

In response to this extended attack, journalists began employing a string of euphemisms. These alternative terms were used instead of the allegedly demagogic term, "Medicare cuts."

No one ever quite explained what was wrong with this traditional term. Medicare "cuts?" This term had always been used, within both parties, to describe budget proposals of the type the GOP had made.

But so what? This non-discussion pseudo-discussion went on, night after night, for well over a year. As journalists scrambled to find softer terms, no one untangled the conceptual mess at the heart of this pseudo-discussion.

In policy terms, this badly bungled pseudo-discussion formed the heart and soul of the non-debate pseudo-debate which led up to November 1996 election, in which President Clinton won re-election over Candidate Dole.

Clinton won, Dole lost. But this non-discussion pseudo-discussion lay at the heart of that campaign. Night after night, for month after month, our journalists and cable news pundits performed a scripted non-conversation which spread confusion all over the land.

This non-conversation was, pure and simple, a semantic dispute. The two parties to this discussion agreed on all relevant facts.

That said, no one came forward to clarify this stultifying conceptual mess. Later, it occurred to us that this had been a good example of the guardians leaving their posts.

No logician ever stepped forward to straighten out that semantic conceptual mess. It fell to us to unpack this nonsense in a Baltimore Sun op-ed.

It fell to us, and to Al Franken, who was then still a comedian. Franken clarified this pitiful mess in a comical but instructive part of his 1996 best-seller, Rush Limbaugh is a Big Fat Idiot and Other Observations.

Two comedians had been able to clarify this braindead semantic dispute! As far as we know, no journalists ever did, except perhaps for Maraniss and Weisskopf—and no professor ever stepped forward to serve in a guardian role.

None of our nation's brilliant logicians stepped in to untangle this mess. No other professor came forward to serve in the guardian role.

A few years later, a similar situation obtained when a twenty-month presidential campaign foundered on the basic logic of paraphrase and quotation.

We refer to Campaign 2000, coverage of which which began in earnest in March 1999. As a few graybeards may still recall, that entire campaign turned on the claim that one of the candidates, Candidate Gore, "had a problem with the truth."

Allegedly, this meant that Candidate Gore was like his boss, President Clinton. Clinton had only recently escaped removal from office in his Senate impeachment trial.

For twenty months, that whole campaign turned on the basic logic of paraphrase and quotation. Starting in March 1999, mainstream journalists, again and again, paraphrased and "quoted" statements by Candidate Gore in ways which were designed to show his "problem with the truth."

Had Al Gore said he invented the Internet? Again and again, for twenty straight months, that's what our journalists said.

Had he said he inspired Love Story? Had he said he discovered Love Canal? Had he said he grew up on a farm, when he really grew up in a fancy hotel—even in the Ritz Carlton?

In September 2000, did the candidate lie when he told a joke about a union lullaby? Did he lie about the cost of his pet dog's arthritis pills?

These claims were widely bruited in September 2000, when new polling had made it seem that Candidate Gore was pulling away from Candidate Bush. Early in October, new claims of new lies appeared in the wake of the first Bush-Gore debate, undermining initial impressions that Gore had outperformed Bush.

Simply put, the acts of bogus paraphrase never stopped. Had the candidate "told Time magazine last year that he enacted the Earned Income Tax Credit, which of course went into law before he was ever in Congress?" Lawrence O'Donnell revived that groaner very late in the campaign, appearing on the high-profile syndicated program, The McLaughlin Group.

AL GORE, LIAR! From March 1999 through November 2000, it was the central "journalistic" narrative of Campaign 2000.

The press corps' crescendo of claims turned on highly tendentious acts of paraphrase and quotation. These presentations raised the most basic questions about the logic of these practices, but no logician rose to serve in the time-honored guardian role.

How silent were the professorial lambs? Back in 1978, Professor Bok had published a widely-praised book, Lying: Moral Choice in Public and Private Life.

As of Campaign 2000, this highly-regarded book was still in print. Indeed, a new paperback edition had appeared in 1989—and another new edition appeared in 1999!

That said, Professor Bok had nothing to say about the claims against Candidate Gore. Needless to say, no other logician or ethicist stepped forward to discuss the endless claims being lodged by our mainstream "press corps." Darlings, it isn't done!

These are just two examples—examples from long ago. That said, people are dead all over the world because these guardians walked off their posts during Campaign 2000. There's no limit on the disgust we should feel for these cosseted, useless figures.

Our logicians and ethicists had nothing to say about these long-running episodes. That said, these professors had long since been reassigned to posts outside the public square—to posts in mahoganied academic lounges, or perhaps to posts in the south of France.

The public was badly in need of their help, but the public's need wouldn't be served.

These guardians' refusal to serve continues to this day. The perpetual silence of these upper-class lambs helped give us our President Trump.

The polis will always need guardians! So Plato declared long ago in his famous though tedious book, The Republic. It represents one of the very few things Plato clearly got right.

The polis needs guardians, Plato declared. Tomorrow, we'll review his statements on this obvious point.

Our logicians and ethicists ought to be serving in a guardian role! But these people walked off their posts long ago. The silence of these useless people will be explored in our posts all week.

Tomorrow: Plato gets it right!

Short, medium and long: Long ago, when this site was still young, we posted three reports, of varying length, concerning the Medicare non-discussion discussion.

"The Speaker's new language" was our Medicare magnum opus. In it, we quoted Franken's book at some length.

Our shortest treatment of the matter bore the attractive title, "A tale of three numbers." For links to our three reports, you can just click here.

In these reports, we unpacked the basics of this semantic gong-show. That said, our nation's famous logicians offered no help at any point in this process.

Our logicians were locked in their aeries, as they have been for some time. Clownishly, they were discussing the set of all sets not members of themselves. Their refusal to serve helps explain how Donald Trump got where he is.

Years later, Paul Krugman linked to one of our Medicare reports to help clarify this matter. We can't remember when he did it, although you could find it on line.

THE INCOMPLETENESS FILE: Digest of reports!

MONDAY, SEPTEMBER 24, 2018

New chapter starts tomorrow: What did Godel demonstrate in his "incompleteness theorems?" Are these theorems useful, important, insightful, even coherent?

Can general readers hope to know the answers to such questions? Below, you see links to last week's reports from the incompleteness file:

Tuesday, September 18: Incompleteness meets incoherence! A lucid writer intones.

Wednesday, September 19: What the Sam Hill is a "logical system?" No general reader will know!

Thursday, September 20: What the heck is a "formal system?" Once again, Joe Average won't know!

Friday, September 21: Do Godel's theorems even make snese? Flying spaghetti monsters!

Tomorrow, we start our award-winning "guardians file." To review reports from all previous files, use links provided below:

Monday, September 10: Digest of reports: The Godel file.

Monday, September 17: Digest of reports: The Platonist file.

Monday, September 24: Digest of reports: The incompleteness file.

BREAKING: The Washington Post gets it right!

SATURDAY, SEPTEMBER 22, 2018

Plus, the Post and the Times get it wrong: All praise to the Washington Post's Joe Heim, who authored an outstanding report in Thursday's print editions.

In our view, it should have been an outstanding front-page report. Instead, it got pushed inside, to page A10, where it was an outstanding report about an appalling state of affairs.

Heim reported on the squalid culture which obtained at DC-area private schools in the 1980s, when Brett M. Kavanaugh was a student at Georgetown Prep. We think you should read every word.

Heim produced an outstanding report about an appalling state of affairs. This morning, the Post offers an outstanding front-page report about the drinking and debauchery, during that era, engaged in by Mark Judge, another victim of Georgetown Prep's appalling culture, and a likely victimizer to boot.

Parts of today's report are simply astounding. The report was written by Fisher and Stein. We think you should read every word, especially the part about former "Marriage and Sex teacher" Bernie Ward.

These were, and are, outstanding reports about a disgraceful state of affairs. That said, one day before Heim's report appeared, the Post offered a peculiar front-page report about Diane Feinstein—a puzzling report which the New York Times has finally matched, and has managed to top, on today's front page.

Let's focus on today's report in the Times. It was written by Nicholas Fandos, who's more than three years out of college. (Harvard, class of 2015.)

These high-flying kids today! Fandos seems troubled by the thought that Feinstein honored a pledge of confidentiality to Christine Blasey Ford, a constituent who says she was the victim of a sexual assault when she was just 15. On this basis, Fandos suggests, at several points, that Feinstein, who is 85, may have been slipping a bit in the noggin when she behaved in this manner—when she honored her pledge to Blasey Ford.

Absent the suggestions of senility, the Washington Post's Sean Sullivan authored an equally puzzling, front-page report on Wednesday. Which part of "I made a pledge of confidentiality" don't these scribes understand?

Reading these scribes' reports, we'll admit that we have no idea. But all week long, we've seen cable news hosts who seemed to be similarly challenged concerning this bone-simple ethical point.

Let's be fair! The idea that Feinstein should have broken her pledge seemed to gain wide purchase in the past week or so—and this wasn't simply a cable news talking-point of the right.

Some Democrats seemed to suggest that Feinstein should have outed Blasey Ford too. In this part of Sullivan's report, he blew right past an obvious irony as he described this state of affairs:

SULLIVAN (9/19/18): Democratic senators on the Judiciary Committee were tepid about Feinstein. "She did her best," said Sen. Mazie Hirono (Hawaii). "I can't fault her," said Sen. Kamala D. Harris (Calif.). "Extremely difficult circumstances," noted Sen. Richard J. Durbin (Ill.)

Privately, some Democratic senators wished that Feinstein had come to them sooner with the allegation, according to a Democrat with direct knowledge of internal Senate dynamics. The Democrat spoke on the condition of anonymity to be candid.

It was late July when Feinstein received the letter from Ford detailing the allegations from decades ago against Kavanaugh. Ford is a constituent of Rep. Anna G. Eshoo (D-Calif.), who relayed the letter to Feinstein.

Ford was insistent on confidentiality. It was not until a private meeting last Wednesday, after a report by the Intercept, that Feinstein revealed the letter to her Democratic colleagues on the Judiciary Committee. In a Washington Post article published Sunday, Ford told her story publicly for the first time.

Based on that passage, some Democrats apparently felt that Feinstein should have broken her pledge to Blasey Ford. In a wonderful bit of unintentional irony, Sullivan attributes that report to "a Democrat with direct knowledge of internal Senate dynamics"—a Democrat who spoke to Sullivan on the basis of a pledge of confidentiality!

Such highly principled people! Later in his report, Sullivan quoted a few of the three million Republicans who have pretended that they never heard about Feinstein's pledge to Blasey Ford. That said, a range of highly principled Democrats also seem to have wandered onto the list of those who favor breaking such a pledge concerning a report of a sexual assault:

SULLIVAN: Feinstein's decision to keep the accusation away from her own party, at a moment when liberals were applying immense pressure to defeat Kavanaugh and moderate Democratic senators were debating whether to support him, has triggered second-guessing among Democrats. Now, some lawmakers simply want to turn the page.

"I'm not going to go back and revisit that," said Sen. Doug Jones (D-Ala.), who represents a Republican state and is up for reelection in 2020. "I just think we need to deal with where we are now, not where we might have been."

[...]

Feinstein's challenger this November is Kevin de León, a state lawmaker running to her left who finished a distant second in California's all-party primary. He slammed Feinstein last week for "failure of leadership" and questioned why she waited to give information about the accusation to the FBI.

Running to Feinstein's left, de Leon thinks a senator should break a pledge of confidentiality to a person like Blasey Ford. In other words, Feinstein should have "outed" Blasey Ford. Just as "Father" once famously did, we lefties now know best!

On the brighter side, Sullivan (like his editor) seems to be ready for a cable news hosting spot. As he records all these criticisms, he challenges no one to reconcile their criticism with the ethics of Feinstein's pledge. But so it went, again and again, on cable news this week.

On cable news this week, somnolent hosts like Anderson Cooper repeatedly let hard-bitten pseudo-conservatives play dumb about the circumstances surrounding Feinstein's behavior. Why didn't she bring it up earlier, these con men kept asking, skipping right past the fact of her pledge with their host's acquiescence.

On Wednesday morning, Sullivan adopted this stance. Today, Fandos takes us one step farther, suggesting that Feinstein honored her pledge because she's getting soft in the head—because she seems to be senile.

This is how Aristotle's "rational animals" will behave when Plato's "guardians" abandon their posts. When our logicians devote their lives to pondering 2 + 2 = 4, children all over the newsosphere are going to reason this way.

Next week: The guardians file

One more example: Last weekend, on AM Joy, Joy Reid and Zerlina Maxwell criticized Feinstein's behavior. They failed to discuss the ethics of breaking a pledge of confidentiality concerning a sexual assault.

Can they explain why Feinstein should have broken her pledge? If so, they didn't bother.

You can see their exchange in the first two minutes of this tape. We no longer expect much better from Reid. We do expect better from Maxwell.

THE INCOMPLETENESS FILE: Do Godel's theorems even make sense?

FRIDAY, SEPTEMBER 21, 2018

Flying spaghetti monsters: Are Godel's "incompleteness theorems" actually "important?"

Do they carry any social significance? In the end, do they even make sense?

We'll admit to being doubters on the last of those points. Consider a part of Rebecca Goldstein's book which we'll explore in more detail at some later point.

Goldstein's book, designed for general readers, appeared in 2005. It bore this title: Incompleteness: The Proof and Paradox of Kurt Godel.

In our view, the general reader won't likely emerge from this book with the ability to discuss these supposedly transplendent theorems. For ourselves, we were surprised by the way Goldstein, a philosophy professor, leaned on the concept of "paradox" in her discussions, not excluding this rumintaion on a famous "abstract object:"

GOLDSTEIN (page 91): Russell's paradox concerns the set of all sets that are not members of themselves. Sets are abstract objects that contain members, and some sets can be members of themselves. For example, the set of all abstract objects is a member of itself, since it is an abstract object. Some sets (most) are not members of themselves. For example, the set of all mathematicians is not itself a mathematician—it's an abstract object—and so is not a member of itself. Now we form the concept of the set of all sets that aren't members of themselves and we ask of ourselves: is it a member of itself?...

Now we form the concept of the set of all sets that aren't members of themselves? But why in the world would we do that?

The paragraph continues from there. The reference to "Russell" is a reference to Lord Russell, eventual husband of Lady Ottoline—that is to say, to Bertrand Russell—who came up with this world-class groaner back in 1901.

When we first encountered Goldstein's book, it surprised us to think that a capable philosophy professor would still be trafficking in this antique hocus-pocus about these "abstract objects"—about "abstract objects" which may or may not be "members of themselves."

We were even more surprised to see her marveling about this pseudo-paradox, which is even more simple-minded:

"This very sentence is false."

Good God! The later Wittgenstein returned to England hoping to remove these flying spaghetti monsters from the pseudo-discourse in which he himself had trafficked as the early Wittgenstein. We were surprised to see a ranking professor still shoveling these snowstorms around.

We'll discuss these matters in the weeks ahead, possibly next week. For ourselves, if Godel's theorems turn on piddle like this, we'll float the shocking possibility that they may not make any real sense.

We know it's shocking to hear such claims about the genius theorems Goldstein gushes about. Then again, this "greatest logicians since Aristotle" seems to have been mentally ill his entire life; eventually died of self-starvation; and believed all sorts of crazy idea, perhaps including the crazy idea that numbers and circles live "a perfect, timeless existence" somewhere, apparently in an "abstract" realm we can access through something resembling ESP.

Do the theorems of this unfortunate man actually make any sense? For now, we'll vote with the doubters. Meanwhile, when Jordan Ellenberg discussed Goldstein's book for Slate, he offered these remarks, among others:

ELLENBERG (3/10/05): In his recent New York Times review of Incompleteness, Edward Rothstein wrote that it’s “difficult to overstate the impact of Gödel’s theorem.” But actually, it’s easy to overstate it: Goldstein does it when she likens the impact of Gödel’s incompleteness theorem to that of relativity and quantum mechanics and calls him “the most famous mathematician that you have most likely never heard of.” But what’s most startling about Gödel’s theorem, given its conceptual importance, is not how much it’s changed mathematics, but how little. No theoretical physicist could start a career today without a thorough understanding of Einstein’s and Heisenberg’s contributions. But most pure mathematicians can easily go through life with only a vague acquaintance with Gödel’s work. So far, I’ve done it myself.

You can read the rest of what Ellenberg wrote. For now, we're just saying!

When our greatest logicians devote their lives to the antics of spaghetti monsters, should we be surprised by the sheer stupidity which obtains all over the national discourse engineered by corporate journalists? We'll be focusing on that question next week. For today, let's visit an early part of Goldstein's book, where she starts to get something right.

When Holt summarized Goldstein's book, he profiled the strangeness of Godel. Again, we ask you to marvel at the highlighted part of this pile:

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...[T]he 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.

Sadly, strangely, possibly dumbly, the greatest minds in Europe were puzzling hard over this:

What makes a proposition like "2 + 2 = 4" true?

Seriously though, folks! From 1901 right up through Godel's arrival at college, that's what our allegedly greatest minds were struggling to figure out!

We mention this for a reason. Near the start of her book, Goldstein gives a weirdly decent explanation of this potent conundrum. She speaks about a different fact—the fact that 5 + 7 = 12—but, as you can probably see, the basic logic of all such statements is pretty much the same.

Citizens, we encountered this same traditional groaner as college freshmen ourselves! How can we know that 7 + 5 = 12? Professor Nozick raised this "problem" in the introductory course, Phil 3: Problems in philosophy.

How do we know that 7 + 5 = 12? One wag in the back of the class dared to ask himself this:

Who is this "problem in philosophy" a problem for?

Or words to that effect! On the world's most exalted comedy stages, we've occasionally recalled one subsequent discussion. We did so just a few years ago, with comedy-loving Clarence Page as an opening act:

PHILOSOPHICALLY TORTURED TEACHING ASSISTANT: Students, how can we know that 7 + 5 equals 12?

INNOCENT FRESHMAN: Miss Cummings told us? In second grade?

FRUSTRATED TEACHING ASSISTANT (tearing his hair as he stares out the window, seeming to contemplate the abyss): No, no, students, you're missing my point! How do we know that 7 + 5 equals 12?

[Pregnant pause]

PUZZLED FRESHMAN: Same answer?

Did that exchange really take place? Memory sometimes plays tricks. But we're fairly sure that we remember the paper we finally wrote on this topic, and it resembled the explanation Goldstein supplies early in her book.

What makes a proposition like “2 + 2 = 4” true? Using a slightly tougher example, Goldstein offers this:

GOLDSTEIN (page 17): The rigor and certainty of the mathematician is arrived at a priori, meaning that the mathematician neither resorts to any observations in arriving at his or her mathematical insights nor do these mathematical insights, in and of themselves, entail observations, so that nothing we experience can undermine the grounds we have for knowing them. No experience would count as grounds for revising, for example, that 5 + 7 = 12. Were we to add up 5 things and 7 things, and get 13 things, we would recount. Should we still, after repeated recountings, get 13 things we would assume that one of the 12 things had split or that we were seeing double or dreaming or even going mad. The truth that 5 + 7 = 12 is used to evaluate counting experiences, not the other way around.

Goldstein is on the right track. That said, and stating the obvious, it makes more sense to explore the logic of this conundrum through the simplest possible example: 1 + 1 = 2.

How do we know that 1 + 1 = 2? Simple! Among other factors, we would be strongly disinclined to accept alleged counterexamples! Let's think in terms of marbles.

"Two" is simply the name we give to the number of marbles you'll typically have if you start with one marble, then receive one additional marble. If you counted your marbles at that point and found you had three marbles, we would assume that you hadn't noticed the addition of the third marble. Beyond that, we wouldn't accept such counterexamples as these:

Haystack Calhoun does the math:
A farmer has one haystack. He adds to it a second haystack. He sees that he still has one (larger) haystack. The farmer declares that, at least on the farm, 1 + 1 = 1.

Porky Pig adds to the wealth:
A farmer has one (male) pig. He adds one (female) pig. Months later, he finds that he has eight pigs. The farmer declares that, at least on the farm, 1 + 1 = 8.

The evaporation monologues:
A chemist has one beaker of a chemical. He adds a second beaker of a different chemical. The beaker's contents go "poof" and all the liquid disappears. When he added the second beaker, he ended up with no beakers. The chemist declares that, at least in the lab, 1 + 1 = 0.

What would we say to such counterexamples? We would say they aren't what we mean! In each case, that simply isn't what we mean when we say 1 + 1 = 2!

How do we know that 1 + 1 = 2? We know it because we know what we mean when we make the familiar statement. All other addition facts follow from there. No flying spaghetti monsters, abstract or not, need apply!

Goldstein made a decent play on page 17. In our view, her book goes downhill from there, biographical writing excluded.

People, one plus one equals two! As our greatest thinkers argued this point, war came to Europe again.

Next week: The guardians file

Now for the rest of the story: After we freshmen took Phil 3, we all decided to abandon philosophy as a major. Nozick, who was only 26 at the time, went on to become a huge star. (He was always very nice to us pitiful freshmen.)

We switched back after sophomore year. Historical inevitability seemed to take over from there.

THE INCOMPLETENESS FILE: What the heck is a "formal system?"

THURSDAY, SEPTEMBER 20, 2018

Once again, Joe Average won't know: Friend, are you a general reader? That is to say, are you a non-specialist in the fields of mathematics, mathematical logic, theoretical physics and the like?

Friend, if you're a general reader, let's consider the title essay of Jim Holt's new book.

The new book is called When Einstein Walked with Godel: Excursions to the Edge of Thought. The title essay is called When Einstein Walked with Godel—and friend, we're telling you this:

Ignore the various things you read about how "readable" Holt's essays are! Friend, if you're a general reader, there is exactly zero chance that you'll emerge from that title essay with even the slightest idea what Kurt Godel's "incompleteness theorems" are alleged to be all about.

As we showed you yesterday, there's zero chance you'll have any idea! Ignore what reviewers have said!

Alas! Several layers of academia, journalism and the publishing world are involved in the creation of this strange state of affairs. Before we look at Rebecca Goldstein's first attempt at explaining Godel's theorems—it's Goldstein's "Godel made easy" book which Holt reviewed in his title essay—let's take a minute to consider, once again, who these high-ranking players are.

We'll start with Godel himself, the man "who has often been called the greatest logician since Aristotle."

Who the Sam Hill was Kurt Godel? As it turns out, he seems to have been mentally ill throughout the whole course of life. (At age 72, he died of self-starvation.)

During his adult years in Princeton, he was famous for believing all sorts of crazy ideas. Among them, perhaps, was his foundational belief in "Platonism"—his ardent belief, in Holt's formulation, that "numbers and circles have a perfect, timeless existence" somewhere. (We're able to access this perfect world through some form of ESP.)

Should it seem strange that our greatest logician can be described in this way? We'll examine that question in more detail next week.

For now, let's continue assembling our list of players. Let's consider the circle of thinkers among whom Godel was moving when he devised his iconic theorems, when he was just 23.

According to the profiles offered by Holt and Goldstein, Godel was moving among the Vienna Circle, a group which is said to have included some of the western world's greatest thinkers. As Europe suffered between two wars, these thinkers were puzzling over how we can know that 2 + 2 = 4. They were also puzzling over how we can know that 4 is an even number.

Later, one of their descendants was puzzling over the question of how we can know that 317 (or 17, or 7) is a prime. Godel, our second greatest logician, was apparently puzzling out these crucial topics too.

Friend, do you find it odd to think that our greatest thinkers were puzzling over such questions? We find that odd (and unimpressive) too, just the way you do!

We find that unimpressive, a point we'll discuss next week. But at this point, we must consider the role in this story which gets played by the publishing industry. We must also consider the work of our own modern-day professors and upper-end journalists.

Our publishing business is awash in "Einstein made easy" books (and the like). None of these books has ever managed to make Einstein easy, including the 1916 "Einstein made easy" book written by Einstein himself.

(Einstein, our greatest theoretical physicist, was not a skilled popular writer.)

No one can understand these books, but professors keep turning them out. They take turns blurbing each other's books, telling us rubes how "lucid" these "accessible" books really are. In response, major reviewers stand in line to say beautifully readable these amazingly easy books are!

As any lover of humor would, we've found this fandango fascinating for a great many years. Next week, we'll consider the real-world problems our savants ignore as they produce unreadable books about 2 + 2 equaling 4 and about how we can know such facts.

Quick question! When our ranking professors behave in these ways, should we really be surprised by the intellectual chaos which characterizes our journalism? When our greatest thinkers behaved (and behave) in these ways, should we really be surprised by the low-IQ mugging and clowning which gets presented on corporate cable each night, as our nation slides into the sea?

(And each morning, on Morning Joe, whose entire panel flipped today concerning the need for an FBI probe of what the accuser has said. The panel moved from yesterday's "no" to today's full-throated "yes." We'd use the accuser's name, except the Times is calling her "Blasey" and the Post is still calling her "Ford.")

When the title essay to his new book first appeared, Holt was reviewing Professor Goldstein's 2005 "Godel made easy" book. Because Goldstein is a highly regarded novelist as well as a ranking philosophy prof, it may have seemed like a great idea to have her write a book about the life and the work of this puzzling, disordered man.

As we noted yesterday, Holt's treatment of the "incompleteness theorems" will be totally incoherent for the general reader. For our money, the general reader won't likely be able to make hide nor hair of Goldstein's treatment either.

Holt wrote a book review for The New Yorker; by way of contrast, Goldstein had written a complete book. In our view, the general reader will have little chance of understanding Godel's theorems from reading that book, but for obvious reasons, we can't reproduce Goldstein's full presentation in the way we could do with Holt.

(We also think the professor went places which we found astounding. "This very sentence is false?" It's stunning to think that ranking professors can still find meaning in places like that. More on that starting tomorrow.)

Where Holt wrote an incoherent essay, Goldstein wrote a hard-to-read book. For our money, the general reader will almost surely emerge from that book with no idea what those "incompleteness theorems" are actually all about.

For today, we'll only show you the way Goldstein introduced the theorems. A person might claim that this is unfair, although we aren't sure it is.

On page 23 of Goldstein's book, she stops discussing Albert Einstein and turns to the young Kurt Godel. As she introduces Godel, she marvels at how young he was when he devised his iconic theorems. She almost seems to say that the theorems are easy to state:

GOLDSTEIN (page 23): He is Kurt Godel, and in 1930, when he was 23, he had produced an extraordinary proof in mathematical logic for something called the incompleteness theorem—actually two logically related incompleteness theorems.

Unlike most mathematical results, Godel’s incompleteness theorems are expressed using no numbers or other symbolic formalisms. Though the nitty-gritty details of the proof are formidably technical, the proof’s overall strategy, delightfully, is not. The two conclusions that emerge at the end of all the formal pyrotechnics are rendered in more or less plain English. The Encyclopedia of Philosophy’s article “Godel’s Theorem” opens with a crisp statement of the two theorems:

Tell the truth! Reading that passage, it sounds like it won't be hard to make Godel easy!

The two conclusions Godel reached "are rendered in more or less plain English," Goldstein writes. "Delightfully," the overall strategy of his proof isn't formidably technical!

Goldstein makes it sound like Godel and his theorems won't be all that hard! Then, she quotes the Encyclopedia of Philosophy's "crisp statement of the two theorems." The passage she quotes goes like this:

GOLDSTEIN (continuing directly): "By Godel's theorem, the following statement is generally meant:

"In any formal system adequate for number theory there exists an undecidable formula—that is, a formula that is not provable and whose negation is not provable. (This statement is occasionally referred to as Godel’s first theorem.)

"A corollary to the theorem is that the consistency of a formal system adequate for number theory cannot be proved within the system. (Sometimes it is this corollary that is referred to as Godel’s theorem; it is also referred to as Godel’s second theorem.)"

That quoted passage is attributed the Encyclopedia of Philosophy. We'll suggest you consider this:

According to Goldstein, this account of Godel's theorems has been "rendered in more or less plain English." We trust and believe that you, a general reader, can see that this just isn't so.

How does the Encyclopedia define or describe the first theorem? In plain English, it goes like this:

In any formal system adequate for number theory there exists an undecidable formula—that is, a formula that is not provable and whose negation is not provable.

Friend, that passage simply isn't written in plain English. We hope you could already see that.

Citizens, can we talk? The general reader will have no idea what a "formal system" is! Beyond that, this general reader will have little idea what "number theory" is.

In part for these reasons, this general reader won't be able to imagine what a formal system "adequate for" number theory is. The general reader will have no idea what that passage is talking about.

However "crisp" this statement may be, this statement will be clear as mud to the general reader. It contains the kind of technical language which may not look like technical language. But this language is guaranteed to leave the general reader on the outside, haplessly looking in.

Briefly, let's be fair. This passage represents Goldstein's first attempt at describing these iconic theorems. This strikes us as a strange first attempt but, at least in theory, Goldstein could have continued on from there to unpack these theorems in a way the average Joe could actually understand.

For our money, that doesn't happen in Goldstein's book. Along came Holt, to offer the crazily incoherent summary we perused in full in yesterday's report.

On page 26, Goldstein reassures the general reader. She does so in this passage, in which she once again plays the "plain English" card:

GOLDSTEIN (page 26): [Godel’s theorems] are the most prolix theorems in the history of mathematics. Though there is disagreement about precisely how much, and precisely what, they say, there is no doubt that they say an awful lot and that what they say extends beyond mathematics, certainly into metamathematics and perhaps even beyond. In fact, the mathematical nature of the theorems is intimately linked with the fact that the Encyclopedia of Philosophy stated them in (more or less) plain English. The concepts of “formal system,” “undecidable,” and “consistency” might be semi-technical and require explication (which is why the reader should not worry if the succinct statement of the theorems yielded little understanding); but they are metamathematical concepts whose explication (which will eventually come) is not rendered in the language of mathematics.

Finally! Three pages later, Goldstein notes that the general reader has no idea what a "formal system" is. For the record, she offers her first definition of the term on page 129 [sic].

In our view, things don't get a whole lot better for the general reader in what follows from there. Things seem technical all the way down. It seems to us that the general reader will likely be forced to quit.

Citizens, let's review:

Our greatest logician was mentally ill and possessed of crazy ideas. At the heart of his prolix theorems was his apparently crazy belief that numbers and circles live a perfect existence somewhere.

In turn, our philosophy professors seem to have no idea how to explain these prolix theorems (which "say an awful lot") to the general reader. But they produce books which claim to have done that anyway. When they do, journalists rush to say that they understood every word. And it all began with our greatest thinkers pondering 2 + 2.

When we see this cultural pattern unfold, are we surprised by the utter incoherence displayed by lesser thinkers on corporate cable? Are we surprised that our broken, pre-rational public discourse has now helped to place a Donald J. Trump in the White House?

Seeing ourselves from afar, we humans still tend to believe, say and suggest that we're the rational animal. In our view, this profoundly iconic notion qualifies as "Aristotle's [gigantic large howling] error."

Tomorrow, we'll debase Godel a tiny bit more, prepping a bit for next week. We'll also see Professor Goldstein do something amazingly rare.

Tomorrow: A (near) perfect statement by Goldstein

THE INCOMPLETENESS FILE: What the Sam Hill is a "logical system?"

WEDNESDAY, SEPTEMBER 19, 2018

No general reader will know: According to the headline on the New York Times review, Jim Holt's new book is a collection of essays which "make sense of the infinite and the infinitesimal."

It's Holt's "conviviality, and a crispness of style, that distinguish him as a popularizer of some very redoubtable mathematics and science,“ the gushing reviewer said, marching in upper-end lockstep.

Indeed, it wasn't just the New York Times making these mandated statements. According to the headline on the Christian Science Monitor review, "When Einstein Walked with Gödel"—that's the title of Holt's new book—"is science writing at its best."

The essays in Holt's new book "all wonderfully achieve [his] stated goal," which includes "enlighten[ing] the newcomer," the Monitor's reviewer said. "This is considerably more difficult than it sounds, and Holt does a beautifully readable job."

Holt's collection of essays wasn't reviewed by the Washington Post, but the reviewer for the Wall Street Journal completed the rule of three. Holt is "one of the very best modern science writers," this third reviewer opined. He specifically singled out Holt's "wonderful title essay."

That's the very essay we've been discussing—the essay in which Holt tries to explain Kurt Godel's "incompleteness theorems."

Reviewers seemed to agree. Holt's work is "beautifully readable," especially for "the newcomer"—for the general reader. But then we turn to that title essay, the one in which Holt attempts to explain Godel's theorems.

According to Holt, those theorems have established Godel, by widespread agreement, as "the greatest logician since Aristotle." An obvious question arises:

How "beautifully readable" is Holt's explanation of those iconic theorems? To what extent is Holt's account of those theorems "science writing at its best?"

As we noted yesterday, Holt explains those theorems in two extremely long paragraphs. As we showed you yesterday, the first of those paragraphs, by far the shorter of the two, reads as shown below in Holt's title essay, which first appeared in The New Yorker in 2005.

Below, you see the first of the two paragraphs in which Holt explains Godel's theorems. By the end of this paragraph, our greatest logician since Aristotle is, for reasons which don't quite get explained, pondering 2 + 2:

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 1920s 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.

As this first long paragraph ends, the greatest thinkers in Europe are puzzling over a knotty problem. According to Holt's own language, they're trying to explain "what makes a proposition like 2 + 2 = 4 true."

Without so much as chortling even once, Holt proceeds from there:

One group of Europe's most brilliant thinkers is said to have said that the truth of 2 + 2 = 4 lies in the fact that "it could be derived in a logical system according to certain rules." Without attempting to explain what that technical word salad means, Holt proceeds to say what the youthful Godel believed:

The youthful Godel is said to have thought that the truth of 2 + 2 = 4 lies in the fact that "it correctly describes some abstract world of numbers"—presumably, the world in which "abstractions like numbers and circles have a perfect, timeless existence independent of the human mind." So the greatest logician thought, as opposed to the other great thinkers.

Scotty, beam us down! Despite the gushing of those reviewers, no general reader will have any idea what that paragraph means.

What does it mean to say that 2 + 2 = 4 "can be derived in a logical system according to certain rules?" No general reader has the slightest idea, but Holt doesn't stop to decipher the claim. He merely compares it to what Godel is said to have thought—a belief which is said to involved the perfect existence of circles.

In these ways, our greatest thinkers puzzled out 2 + 2. Last May, major journalists stood in line to say how "beautifully readable" Holt's new book is, especially the "wonderful title essay" in which this hodgepodge appears.

In such ways, we see a modern, high-end display of "Aristotle's error." These reviewers aren't reflecting the ancient claim that "man [sic] is the rational animal." Rather, they're acting out the "Harari heuristic," which holds that our warlike species, Homo sapiens, gained control of the planet when, through a set of chance mutations, our ancestors developed the ability to "gossip" and the ability to invent and affirm sweeping group "fictions."

As the weeks and months proceed, we'll return to Harari's account, reviewing his claims in more detail. For today, we'll only note an obvious fact—even by the end of this first paragraph, Holt's opaque, highly technical writing will have left any general reader several light-years behind.

Alas! Whether they know it or not, general readers will already be at sea by the end of that first paragraph. Most specifically, such readers will have no idea what a "logical system" is.

Nor will such readers have any idea what it means to say that a nursery school fact like 2 + 2 "can be derived in a logical system according to certain rules." Already, Holt may as well be writing in some form of ancient Etruscan.

In the paragraph which follows, Holt starts explaining those "incompleteness theorems." When he does, a large pile of Sandstorm arrives.

At the end of this pig-pile of abstruse phrases, Godel's two theorems get defined. The general reader will have zero idea what Holt is talking about:

HOLT (continuing directly): Gödel was introduced into the Vienna Circle by one of his professors, but he kept quiet about his Platonist views. Being both rigorous and averse to controversy, he did not like to argue his convictions unless he had an airtight way of demonstrating that they were valid. But how could one demonstrate that mathematics could not be reduced to the artifices of logic? Gödel’s strategy—one of preternatural cleverness and, in the words of philosopher Rebecca Goldstein, “heart-stopping beauty”—was to use logic against itself. Beginning with a logical system for mathematics, one presumed to be free of contradictions, he invented an ingenious scheme that allowed the formulas in it to engage in a sort of doublespeak. A formula that said something about numbers could also, in this scheme, be interpreted as saying something about other formulas and how they were logically related to one another. In fact, as Gödel showed, a numerical formula could even be made to say something about itself. Having painstakingly built this apparatus of mathematical self-reference, Gödel came up with an astonishing twist: he produced a formula that, while ostensibly saying something about numbers, also says, “I am not provable.” At first, this looks like a paradox, recalling as it does the proverbial Cretan who announces, “All Cretans are liars.” But Gödel’s self-referential formula comments on its provability, not on its truthfulness. Could it be lying when it asserts, "I am nor provable?" No, because if it were, that would mean it could be proved, which would make it true. So, in asserting that it cannot be proved, it has to be telling the truth. But the truth of this proposition can be seen only from outside the logical system. Inside the system, it is neither provable nor disprovable. The system, then, is incomplete. The conclusion—that no logical system can capture all the truths of mathematics—is known as the first incompleteness theorem. Gödel also proved that no logical system for mathematics could, by its own devices, be shown to be free from inconsistency, a result known as the second incompleteness theorem.

Ar the end of this, the world's longest paragraph, Holt defines, or pretends to define, Godel's two "incompleteness theorems." Despite the subsequent, mandated gushing of our journalistic elites, no general reader will have any idea what Holt is talking about.

Consider the various snares and traps that reader has encountered during this long forced march to the sea:

We're told that Godel wanted to demonstrate that "mathematics could not be reduced to the artifices of logic." The general reader will have no idea what such a reduction might look like.

In pursuit of this puzzling end, we're told that Godel "beg[an] with a logical system for mathematics, one presumed to be free of contradictions." The general reader won't know what "a logical system" is. He won't know what it means for such a creature to be "adequate for mathematics."

We're now told that Godel came up with "a formula that said something about numbers." On the pain of impending death, the general reader won't be able to imagine an example of any such formula making any such statement. Nor will she have any idea what it might mean to produce "a formula that, while ostensibly saying something about numbers, also says, 'I am not provable.' ”

A bit later on, the reader seems to be told that Godel produced "a self-referential formula" which generated a proposition whose truth "can be seen only from outside the logical system." No general reader has any idea what Holt is talking about.

At any rate, atthe end of this long harangue, Holt describes Godel's first incompleteness theorem. Excitement builds for the general reader. Then he's told that the theorem says this:

"No logical system can capture all the truths of mathematics."

That would be an exciting claim. Except, do you remember the problem with which the general reader started? He or she has no idea what a "logical system" is!

In these two paragraphs, Holt explains, or pretends or attempts to explain, Godel's two "incompleteness theorems." For unknown reasons, this Olympian hodgepodge was first offered to general readers in the pages of The New Yorker. Few subscribers could have had any idea what Holt was talking about.

Thirteen years later, Holt's piece was published as the title essay in a collection of his work. Mainstream reviewers stood in line to praise it for being readable, especially for newcomers to the subject matter.

What a long, strange journey it has been through those lengthy paragraphs! We started with Europe's greatest thinkers pondering the fact that 2 + 2 equals 4. We were told that the greatest logician since Aristotle believed that circles and numbers and other such critters have a perfect, timeless existence, an existence we can access through some version of ESP.

Eventually, an avalanche of technical language landed on our newcomer heads. But so what? An obedient line of upper-end journalists said this all made perfect sense.

We're going to say that all these groups are providing textbook illustrations of "Aristotle's error." Also this:

When our journalists behave in the manner described, they're helping us see how things fall apart when Plato's guardians fail.

Tomorrow: Goldstein's first attempt

THE INCOMPLETENESS FILE: Incompleteness meets incoherence!

TUESDAY, SEPTEMBER 18, 2018

Lucid writer intones: Subscribers to The New Yorker had a major treat in store.

Or at least, so it seemed.

Their February 28, 2005 issue had arrived in the mail. It featured a lengthy essay in which a writer named Jim Holt discussed a pair of new books.

One of the books concerned Albert Einstein, an extremely famous theoretical physicist. The other new book concerned Kurt Godel, a "logician" who isn't well-known by the average shlub at all.

This May, Holt's New Yorker essay, lightly edited, reappeared as the title essay in his own new book, When Einstein Walked with Godel: Excursions to the Edge of Thought.

As seems to be required by law, Holt's new book was praised by major reviewers—was praised for its lucidity. In the thirteen years since that essay appeared, Holt had become a "made man" in New York publishing circles.

Within those circles, Holt is now reflexively praised for the clarity of his writing about difficult science and math. As you can see, Wikipedia even headlines him as a "philosopher!" That's how silly and mandatory this sort of thing has become.

Holt's book of essays was praised this year for its brilliant lucidity. As we noted last Friday, the same was true of the new book about Kurt Godel which he discussed in The New Yorker back in 2005.

Hurrah! That new book, by Rebecca Goldstein, had been described as "accessible"—but also as "surprisingly accessible," even as "remarkably accessible."

It had been praised as a "lucid expression" of Godel's ideas—but it had also been hailed as "eminently lucid." So it goes within our tightly scripted academic journalistical complex.

Goldstein's treatment of Godel's ideas had been widely praised. Now, a writer at The New Yorker was going to boil matters down even further! Subscribers would finally get a chance to understand Godel's "incompleteness theorems," on the basis of which, Holt now said, Godel has often been called "the greatest logician since Aristotle."

Truth to tell, nothing dimly resembling that occurred in Holt's piece. In fairness, Goldstein hadn't been especially lucid when it came to explaining Godel's theorems either.

For the general reader, Goldstein's treatment of Godel's theorems would almost surely have been extremely hard to follow. When Holt took his turn in The New Yorker, his attempt to describe those "incompleteness theorems" was almost comically incoherent—incoherent all the way down.

Today, the book by Holt which features that essay is being praised by major journalists for its brilliant clarity. In this way, a comical aspect of our journalism—indeed, of our upper-end culture's most basic attempt at rationality—has once again been put on display, for perhaps the ten millionth time.

Holt's essay appeared in early 2005. Its author discussed Einstein's theory of relativity, then turned to Godel's theorems. In this week's reports, we'll speak of Godel alone.

Back in May, readers of the New York Times and the Wall Street Journal were told that Holt's rather obvious incoherence is an example of brilliant lucidity.

In this way, we've been given another look at the classic misassessment we've now christened as "Aristotle's error." We've been given another look at the way we humans, at least in the west, keep "seeing ourselves from afar."

Thanks to his incompleteness theorems, Godel has often been described as the greatest logician since Aristotle. But what did Godel actually say in his theorems? What was he trying to show?

In his essay for The New Yorker, Holt addressed those basic questions in two enormously long paragraphs. Today, we'll examine the first of those paragraphs, transcribing it as it appears in Holt's current book.

We'll start with an apology. In the past two weeks, we've already posted the start of the first paragraph in question. Before we show you Holt's full paragraph, we'll revisit that part, for review:

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...

According to Holt, Godel had come to believe that "abstractions like numbers and circles had a perfect, timeless existence independent of the human mind." As it turns out, Godel was "seduced" by this "doctrine" as a mere freshman in college.

Already, a perceptive reader might suspect that she's being directed by "a guide...who only has at heart [her] getting lost." What in the world does a person believe when he believes that "numbers and circles have a perfect, timeless existence independent of the human mind?" What does it mean to "believe," to be seduced by, such a peculiar notion?

Already, a perceptive reader should be asking such questions. But Holt just kept plowing ahead.

In the passage we've posted above, Holt said that's what Godel believed. He didn't try to explain what that peculiar formulation might possibly mean. Instead, he moved on to describe a major dispute within the intellectual world of Godel's Vienna.

What follows is the first of the two lengthy paragraphs in which Holt explains, or attempts or pretends to explain, Godel's "incompleteness theorems." Warning! The second graf, which we'll review tomorrow, is almost twice as long as the first.

According to recent reviews in the Times and the Journal, this paragraph appears within the title essay of a book in which the writing is brilliantly incisive and clear. Additional warning! By the end of this paragraph, the greatest logician since Aristotle is asking himself how we can know that 2 + 2 equals 4!

That's what Godel is asking himself! People, we're just saying:

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 1920s 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.

What makes a proposition like “2 + 2 = 4” true?

As the people of Europe struggled and groaned between two deeply destructive world wars, that's the type of question the western world's most brilliant thinkers were laboring to resolve!

You've now seen the first of the two paragraphs in which Holt explains, or attempts to explain, Godel's "incompleteness theorems." In this first paragraph, Holt basically sets the stage for his ultimate explanation. That will come in the second paragraph, which is roughly twice as long.

What makes a proposition like “2 + 2 = 4” true? In this, the first of his two paragraphs, Holt—the brilliant, incisive writer—sets the stage for spelling it out. This is what he has said:

According to one group of thinkers in Godel's Vienna, "2 + 2 = 4" is true because this rather familiar arithmetical proposition "can be derived in a logical system according to certain rules."

Tell the truth, dear general reader: Do you have the slightest idea what that statement means?

Tell the truth, New Yorker subscriber: Do you understand what it means, even in a general sense, to "derive [an arithmetical proposition] in a logical system according to certain rules?"

Friend, of course you don't! But if that's what one group of thinkers were thinking, at least one other brilliant thinker was brilliantly thinking this:

According to the greatest logician since Aristotle, "2 + 2 = 4" is true because it "correctly describes [an] abstract world of numbers." Perhaps more precisely, it correctly describes one aspect of the perfect, timeless existence enjoyed by numbers and circles outside the human mind!

Europe was struggling between two wars. Tearing their hair in the loftiest circles, the western world's most brilliant "thinkers" were laboring over this.

That being said, did Holt go on to make Godel's approach to this matter brilliantly clear? More specifically, was he able to explain Godel's "incompleteness theorems" in a way the general reader might find wonderfully clear?

That's what major reviewers have suggested. But at this point, does any of this seem especially clear?

Tomorrow, we're going to ask you to strap yourselves into your seats. We'll quickly revisit this first paragraph, into which a substantial amount of incoherence has already been poured.

Then, we'll look at Godel's endless succeeding paragraph, in which he attempts to describe the working of Godel's theorems in a way the general reader will be able to comprehend.

We humans! Seeing ourselves from afar once again, major reviewers have seemed to say that Holt did a wonderful job!

Tomorrow: "Beginning with a logical system for mathematics..."