WEDNESDAY, MAY 19, 2021
...1 + 1 meets the wage gap: As we noted yesterday, Bertrand Russell discussed the true meaning of 1 + 1 in his classic 1903 text, The Principles of Mathematics.
He did so on page 6 of the text—and the text began on page 3!
More precisely, Russell defined the true meaning of "1 + 1 = 2." As you may recall, he said this:
1 + 1 = 2 appears neither to contain variables nor to assert an implication. But as a matter of fact, as will be shown in Part II, the true meaning of this proposition is: “If x is one and y is one, and x differs from y, then x and y are two.”
As he continued, he stated his point in a different way:
Thus the above proposition may be expressed in the form: “Any unit and any other unit are two units.”
For fuller passages from Russell's text, see yesterday's report.
It's easy to make fun of such work. Today, we'll note that Russell's pursuit of 1 + 1 continued in his later, more significant text, Principia Mathematica (1910-1913), which he co-wrote with Alfred North Whitehead.
In 2009, the Modern Library rated the three-volume Principia #23 in its list of the top 100 English-language nonfiction books of the twentieth century. That said, the leading authority on that work displays an excerpt where Russell and Whitehead append the following comment to a rather abstruse chain of symbolic logic:
"From this proposition it will follow, when arithmetical addition has been defined, that 1 + 1 = 2."
You can see the abstruse passage in question simply by clicking this link, then scrolling down a small tad.
It's easy to make fun of such work. But was there, and is there, some actual point to such deliberations?
Frankly, we have no idea, in part because specialists in the field seem to have a very hard time offering accounts of such work which will make any sense at all to the general reader. As we've noted many times in the past, explanation is hard!
For us, these deliberations started early last week. Why did we dig out our old copy of The Principles of Mathematics, trying to see, or perhaps to recall, what Russell's endeavor was all about?
We'd gone there based on something we read in our "most interesting" book of the past twenty years. We refer to Professor Goldstein's 2005 general interest work, Incompleteness: The Proof and Paradox of Kurt Gödel.
By our lights, Professor Goldstein's account of Russell's work, and the academic motives behind it, was so abstruse—so incomprehensible—that we decided to go back and take a quick look for ourselves. But why were we revisiting Goldstein's book, which includes some of the most puzzling revelations we have ever encountered?
We're going to blame it on Petula Dvorak—more specifically, on her column in the Washington Post about the gender wage / pay / earnings gap. In fairness, though, it's time for a confession:
In recent weeks, we'd been finding it harder and harder to endure the banality of "cable news," or to confront the steady-state lack of analytical skill on display in Our Town's leading newspapers.
The banality of Our Town's discourse was harder and harder to take. Then, along came Dvorak's treatment of one of the Our Town's favorite pieces of tribal dogma.
For the record, we take it as obvious that Dvorak is a good, decent person. That said, she seems to be extremely beholden to Our Town's preferred Storylines—or at least, so it seems around here.
One such treasured Storyline involves the gender wage gap, whose ontology our warriors love to misstate. With that in mind, we give Dvorka credit:
As she opened her column, she kept her claims technically accurate. When it comes to the gender wage gap, that's something Our Town's thought leaders frequently fail to do.
Her column had a Mother's Day hook. Hard-copy headline included, here's the way it started:
DVORAK (5/7/21): The best Mother’s Day gift? Equal pay.
Flower's? Scented candles? Brunch?
Nice Mother’s Day gifts, sure. But what America’s moms really deserve—and want—is their 25 cents.
You’ve already heard about the gender wage gap, how women make 82 cents for every dollar a man makes.
But wait until you hear how insanely inequitable it is for mothers—on average, moms in the full-time, American workforce make 75 cents for every dollar a dad makes. And the coronavirus pandemic is making that gap so much worse.
Dvorak did say that this shortfall in wages in "insanely inequitable." She did say that America's moms "deserve" that 25 cents.
That said, let's give credit where due! She didn't say that women were paid 82 cents on the dollars for doing the same (or equal) work. She didn't directly state that familiar part of the tribal talking-point.
Dvorak didn't include that extra phrase—the extra phrase Rachel Maddow included on her famous Meet the Press debacle, which she spent thirty minutes explaining away the next night. Dvorak said that women earn less than men—but she didn't claim that they encounter that 18- or 25-cent gap while doing the same or equal work.
At this site, we can teach Dvorak's omission flat or round. On the one hand, her omission of that phrase kept her statements technically accurate. Her omission of that phrase meant that her statements weren't false.
On the other hand, her avoidance of that common phrase suggests an unflattering possibility:
It suggests the possibility that she knows the facts about this treasured talking-point—that she was willing to mislead her readers, just so long as she didn't make a flatly inaccurate statement.
We can't tell you what Dvorak was thinking as she composed her column. We can tell you what came next.
In her first four grafs, she was advancing a familiar misconception without ever stating it herself. In her next paragraph, she offered a groaning pre-rebuttal rebuttal. Her column continued like this:
DVORAK (continuing directly): Hold on, men who are already pecking out their nastygrams, mansplaining that the wage gap exists because moms stay home or go part-time while they raise your spawn, so that break in employment is actually what creates the Wage Gap Gulch.
Yes and no. Even as teens, women make less than men. At the start of this year, the median weekly wage for male 16- to 19-year-olds was $511. For female teens, it was $467, according to the Bureau of Labor Statistics.
In fact, such breaks in employment are one factor, though they aren't the only factor, in creating that overall earnings gap. As she continued, Dvorak kept suggesting that women get shortchanged in some inappropriate way even when they're teens.
No, she didn't explicitly say that. But that was what she was clearly suggesting—and when we clicked to her Bureau of Labor Statistics, we quickly hit upon two explicit disclaimers saying the statistics shouldn't be used for the very type of comparison Dvorak seemed to be making.
You can find those explicit statements yourself if you choose to click. The kill shot in Dvorak's column was that pitiful pre-rebuttal aimed at those who might try to "mansplain" any such point.
Truly, that's pitiful / hopeless. But so it now endlessly goes at the major news orgs here in Our hapless Town.
At some point, the foolishness grows so deep that even we may come to see that it's time to step away from the serial nonsense. Even we may come to feel that the anthropologists have been right all along—that they've been right when they've told us this:
We humans are the tribal animal. At times of tribal division and societal stress, our brains are wired to churn Storyline while damning The Others, full and complete total stop.
Despondent top anthropologists have constantly told us that. Sometimes, the evidences becomes so comically vast that even we may come to see that there's no point in laboring on.
Dvorak was penning a tribally pleasing bit of agitprop this day. To appearances, she wasn't willing to say things which were flatly false—but she was willing to settle for "grossly misleading."
In her mind, she could apparently hear the corrections or challenges coming! So she penned a pre-rebuttal, relying on the kind of rebuttal-by-identity group which now holds enormous sway in the sillybill streets of Our Town.
No, we didn't decide to quit just because of that column! But at some point, even the most determined guide will temporarily come to feel that the game has been lost. (We think of Plato's Seventh Letter, or of Harrison Ford in Witness.)
On cable news, the usual suspects were churning the usual pap about locking Others up. In the Washington Post, a string of columnists churned tribal dogma, though no single piece of work put us over the top.
Still, we decided it was time to turn to the loftier stuff. And a reasonable length of time had passed since we'd thumbed through Goldstein's book.
We decided to revisit our favorite passages, wondering how they'd seem. Tomorrow, we'll show you what we found there—but soon we were on to Lord Russell's work, including his ruminations on the true meaning of 1 + 1.
It's possible to imagine that there actually was a point to this strain of high-end work. That said, the later Wittgenstein finally walked away from such work:
"Back out of all this now too much for us," as Robert Frost once wrote.
Did Lord Russell's work make sense, or was the later Wittgenstein right? More strikingly, could the claims of top anthropologists possibly be correct? Is it possible that our brains weren't made for most analytical work?
Tomorrow: "The mind crashes," she strangely said. Why in the world would she say that?
Concerning the actual gender wage / pay / earnings gap: It's been explained a million times, for the most part to no avail.
We humans cling to our Storylines! If you're interested in the apparent true state of the gender wage / pay / earnings gap, you should start noodling around.