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September 19th, 2021 (Permalink)

What's New? The Fallacy of the Sheep is!

While writing the previous entry I was somewhat surprised to discover that it was the fourth example over the last ten years of the fallacy of the sheep, yet I didn't have a separate entry for that fallacy. So, now I've filled that lacuna. You can access the new entry from either the Taxonomy on the Main Menu, or the drop-down menu of the alphabetized fallacy entries, both available in the navigational frame to your left. Check it out!

September 16th, 2021 (Permalink)

"Breakthrough" Infections and the Fallacy of the Sheep

…[T]he operator of a diner…offered rabbit sandwiches at a remarkably low price. When questioned about it, he admitted that he used some horse meat to keep his costs down. "But I mix 'em fifty-fifty," he avowed. "One horse to one rabbit."1

In the last few months we've started hearing a lot about "breakthrough" infections. Google Trends shows that the number of searches for the phrase "breakthrough infection" was almost none before April of this year, then peaked in the first week of last month, has declined some since, but remains much higher than before April2. What exactly is a "breakthrough" infection?

A breakthrough infection is simply one in which a vaccinated person becomes infected with the virus the vaccine protects against; it does not mean that the person has any symptoms of the disease3. Since no vaccine is 100% effective in preventing infection, there will always be some breakthrough infections.

Nonetheless, recent events have led to some alarm about coronavirus breakthrough infections: in late June, it was reported that nearly half of new cases in Israel were in people who were vaccinated4, and 75% of those infected in Provincetown, Massachusetts a month later were also vaccinated5.

Some people have misinterpreted these statistics to mean that the vaccinated are just as likely, or even more likely, to become infected than the unvaccinated6. Doing so, however, commits the fallacy of the sheep7.

You may have heard the old riddle: Why do white sheep eat more than black sheep? Because there are more of them. It's not a very good riddle, but it illustrates an important point. When comparing two or more classes of things, you should take into consideration the size of the classes compared. Unless the two classes are the same size, comparing the absolute numbers of a characteristic, such as an infection, between the two classes will be misleading8.

In the case of Israel noted above, the fact that half of those infected were vaccinated and half were unvaccinated, does not mean that the former were just as likely to be infected as the latter. Israel has a high rate of vaccination, with about two-thirds of Israelis having received at least one dose of a vaccine, and about 90% of those being fully vaccinated, at the time of the report9. This means that there were at least twice as many vaccinated Israelis than unvaccinated, yet only half of the new cases were in those vaccinated. Similarly, close to 95% of the population of Provincetown was vaccinated, yet only three-quarters of those infected10. So, there were more white sheep than black ones.

It's likely that we will see more breakthrough infections in coming months as the rate of vaccination continues to increase. So, when you read reports about breakthrough infections in a particular area, always look for the rate of vaccination there. The higher that rate, the higher the percentage of all infections will be breakthrough ones.


  1. Darrel Huff, The Complete How to Figure it: Using Math in Everyday Life (1996), p. 391.
  2. "breakthrough infection", Google Trends, accessed: 9/16/2021.
  3. See:
  4. Marianne Guenot, "Israel says the Delta variant is infecting vaccinated people, representing as many as 50% of new cases. But they're less severe.", Business Insider, 6/24/2021.
  5. Kristina Fiore, "No, Most COVID Infections Are Not Occurring in Vaccinated People", MedPage Today, 8/6/2021.
  6. Jessica McDonald, "Posts Misinterpret CDC's Provincetown COVID-19 Outbreak Report", Fact Check, 8/6/2021.
  7. Stephen K. Campbell, Flaws and Fallacies in Statistical Thinking (1974), pp. 101-104. For other examples of the fallacy, see:
  8. Katelyn Jetelina calls the mistake "base rate bias" or "the base rate fallacy"―see the entry for the latter from the drop-down menu to your left. I'm not sure what "base rate bias" refers to, but I don't think that this is an example of the fallacy of the same name. The base rate fallacy and the fallacy of the sheep are similar, but the latter is a better match for the mistake committed here. See: Katelyn Jetelina, "Israel, 50% of infected are vaccinated, and base rate bias", Your Local Epidemiologist, 6/27/2021.
  9. Edouard Mathieu & Hannah Ritchie, "Vaccinations and COVID-19―Data for Israel", Our World in Data, 2/8/2021. See the charts; accessed: 9/16/2021.
  10. Ellen Barry & Beth Treffeisen, "'It's Nowhere Near Over': A Beach Town's Gust of Freedom, Then a U-turn", The New York Times, 7/31/2021. The outbreak took place due to an influx of visitors to the town, and 80% of the infections due to the event were in such visitors, but I haven't been able to find out what percentage of those visitors were vaccinated. Presumably that percentage was less than 95%, so that the overall percentage of vaccination among those in the town at the time of the outbreak would also be less, but how much less I don't know.

The March Hare, the Dormouse, and the Mad Hatter
September 11th, 2021 (Permalink)

Play with Your Mind, Part 2

Note: Here's an example of the second of the two types of logic puzzle found in this month's new book, Games for Your Mind1, namely, a "knights and knaves" puzzle. Specifically, it's from the master of this type of puzzle, Raymond Smullyan:

…Alice [and] the Duchess…had the following remarkable conversation.

"The Cheshire Cat says that everyone here is mad," said Alice. "Is that really true?"

"Of course not," replied the Duchess. "If that were really true, then the Cat would also be mad, hence you could not rely on what it said."

This sounded perfectly logical to Alice.

"But I'll tell you a great secret, my dear," continued the Duchess. "Half the creatures around here are mad―totally mad!"

"That doesn't surprise me," said Alice, "many have seemed quite mad to me!"

"When I said totally mad," continued the Duchess, quite ignoring Alice's remark, "I meant exactly what I said: They are completely deluded! All their beliefs are wrong―not just some, but all. Everything true they believe to be false and everything false they believe to be true." …

"What about the sane people around here?… I guess most of their beliefs are right but some of them are wrong?"

"Oh, no, no!" said the Duchess most emphatically. "That may be true where you come from, but around here the sane people are one hundred percent accurate in their beliefs! Everything true they know to be true and everything false they know to be false."

Alice thought this over. "Which ones around here are sane and which ones are mad?" asked Alice. … "I've always wondered about the March Hare, the Hatter, and the Dormouse," said Alice. "The Hatter is called the Mad Hatter, but is he really mad? And what about the March Hare and the Dormouse?"

"Well," replied the Duchess, "the Hatter once expressed the belief that the March Hare does not believe that all three of them are sane. Also, the Dormouse believes that the March Hare is sane."2

Are the Mad Hatter, March Hare, and the Dormouse mad or sane?


  1. Playing with Your Mind, 9/7/2021
  2. Raymond Smullyan, Alice in Puzzle-Land: A Carollian Tale for Children Under Eighty (1982), pp. 20-22 & 24-25
  3. Ibid., pp. 146-147

September 8th, 2021 (Permalink)

Play with Your Mind, Part 1

Here's an example of one of the two types of logic puzzle found in this month's new book, Games for Your Mind1. This one was created by Lewis Carroll of Alice in Wonderland fame2. Consider the following clues:

  1. Every one who is sane can do Logic.
  2. No lunatics are fit to serve on a jury.
  3. None of your sons can do Logic.

Based on the above clues, are any of your sons fit to serve on a jury?


  1. Playing with Your Mind, 9/7/2021
  2. Lewis Carroll, Symbolic Logic and the Game of Logic (1958), pp. 112 & 132

New Book
September 7th, 2021 (Permalink)

Playing with Your Mind

Quote: "Among mathematical recreations generally, logic puzzles are the most ecumenical. All that is needed is a bit of patience and some clear thinking. No algebra, geometry, computational skill, or any other sort of specialized knowledge is required. The payoff for solving one, however, is the smile you wear on your face for the rest of the day."1

Title: Games for Your Mind

Subtitle: The History and Future of Logic Puzzles

Author: Jason Rosenhouse

Comment: Rosenhouse is a professor of mathematics who has written a previous book on the Monty Hall problem that I haven't read.

Date: 2020

Summary: Despite its subtitle, this book seems to be more an introduction to logic through puzzles than a discussion of their history or future. It's focused on two types of puzzle, rather than on all those that could be labelled "logic puzzles":

  1. Puzzles based on Aristotelian categorical logic. In particular, the book concentrates on puzzles created by Lewis Carroll, who is better known as the author of the Alice children's books than as a puzzle creator.
  2. What are traditionally called "knights and knaves" puzzles in which there are two types of character, "knights" that always tell the truth and "knaves" that always lie. The late Raymond Smullyan was the master of this type of puzzle, writing several books filled with them.

I've offered a number of puzzles of both types here on the weblog, including the recent "New Logicians' Club" puzzles, which are variations on the second type. Other common types of logic puzzle receive only passing mention in the book. You won't find much on Sudoku puzzles, despite the fact that they are currently the most popular type of logic puzzle. However, Rosenhouse has co-written an entire book on them2, so check that out if Sudoku seriously interests you.

Rather to my disappointment, another common type of puzzle that is largely missing is that which often goes by the name "logic puzzle"―there doesn't seem to be a more specific name for them. There are whole books and magazines devoted to this type of puzzle. Familiar examples are the Smith, Jones, and Robinson puzzle, and the Zebra puzzle―Rosenhouse does give a version of the latter as an example.

If you're interested in learning logic, but don't want to take a class or are daunted by the prospect of reading a text book, and if you enjoy puzzles, you might try this approach. You will, in fact, learn much more from working logic problems than just passively reading a book.

What little I've read of the book is clearly and accurately written, though perhaps aimed at a somewhat more sophisticated readership than I would have expected. For instance, there's a section of the first chapter on philosophy of logic3 that I would suggest skipping unless you're really interested in the topic. In fact, it wouldn't hurt to just skip the whole first chapter and get right to the puzzles in chapter 2.

Disclaimer: This book is from late last year, so it's not brand new, but I haven't read it in its entirety yet. My comments above are based on reading a short excerpt and studying its table of contents.


  1. Section 2.2
  2. Jason Rosenhouse & Laura Taalman, Taking Sudoku Seriously: The Math Behind the World's Most Popular Pencil Puzzle (2012)
  3. Section 1.2

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Recommended Reading
August 31st, 2021 (Permalink)

"Noble Lies" & The Pandemic of Panic

[Socrates:] "…[S]urely we must value truthfulness highly. For if we were right…that falsehood is…only useful to men as a kind of medicine, it's clearly a kind of medicine that should be entrusted to doctors and not to laymen. … It will be for the rulers of our city, then, if anyone, to use falsehood in dealing with citizen or enemy for the good of the State; no one else must do so. And if any citizen lies to our rulers, we shall regard it as a still graver offense than it is for a patient to lie to his doctor…. And so if anyone else is found in our state telling lies…he will be punished for introducing a practice likely to capsize and wreck the ship of state."1


  1. Plato, The Republic, translated by Desmond Lee (2nd edition, 1974), 389b-c
  2. See: The Black-or-White Fallacy
  3. See: March Madness, 3/28/2020

Disclaimer: I don't necessarily agree with everything in these articles, but I think they're worth reading as a whole. In abridging them, I have sometimes changed the paragraphing and rearranged the order of the excerpts in order to emphasize points.

August 27th, 2021 (Permalink)

Fact-Checkers ≠ Lie-Detectors

Unlike previous entries in the fact-checking series1, this one is focused on professional, as opposed to amateur, fact checking. Though the focus will be on the professionals, it relates to the amateurs in that it warns against making a mistake that the pros have made.

Some professional fact-checking organizations use rating systems that suggest that they are capable of detecting lies. For instance, the PolitiFact political fact-checking outfit uses a system it calls a "Truth-O-Meter", and the lowest rating on that system is "Pants on Fire!"2 The phrase "pants on fire" comes, of course, from the schoolyard taunt: "Liar, liar, pants on fire!" Thus, rating a claim "Pants on Fire!" suggests that the person who made the claim was lying. In addition, every year PolitiFact designates a "Lie of the Year". For an example from a different fact-checking group, The Washington Post's Fact Checker uses a rating system called "The Pinocchio Test"3, which is named after the puppet from the children's story whose nose grew when he told a lie.

In most circumstances, the charge of lying is one that carries a strong moral condemnation. As a result, no one should toss around such a charge lightly, and it is itself immoral to do so without supporting it with strong evidence. Unfortunately for the fact checkers, here's why it's usually not possible to do so:

There are three individually necessary and jointly sufficient conditions of lying:

  1. Telling a falsehood: This condition is rather obvious, though some have suggested that you can lie with the truth. Of course, you can deceive people with half-truths just as much as with whole lies, but that just means that lying is not the only way to fool people. The famous legal oath to tell "the truth, the whole truth, and nothing but the truth" makes use of the distinction between half-truths and lies: the last of the three requirements forbids lying, whereas the second one rules out telling half-truths.

    Another way in which it's been suggested that you can lie with a truth is if you believe it to be false. For instance, suppose that a boy believes that today is a school day, but tells his mother that there's no school today. If it turns out that today is, in fact, a school holiday, would what he told his mother be a lie? Certainly, he intended to lie, and we may want to morally condemn him as strongly as if he really did do so. But it's best to preserve the logical distinction between actual lies, half-truths, and attempted lies, even though there may be no moral distinction.

  2. Knowledge of falsity: While speaking falsely is a necessary condition for lying, it is not sufficient. If you say something false while believing it to be true, that is not a lie but a mistake. If you speak falsely without being sure whether what you say is true, then you may be speaking with reckless disregard for the truth, but not lying. Lying requires that you knowingly speak falsely4.
  3. Intent to deceive: Speaking a falsehood while knowing it's false is still not sufficient for lying, for one further condition must be met. Novelists, actors, and comedians may knowingly tell false stories, but we do not morally condemn them as long as there is no intent to deceive. Of course, an actor in a play knowingly speaks falsehoods, but the audience knows just as well as the performer that it is make-believe. While we may suspend disbelief while reading a novel or watching a movie, when it is over we are aware that it was untrue. Such knowing falsehoods are not lies because they are told without an intent to deceive the audience.

To sum up, a lie is a falsehood that is knowingly told with an intent to deceive. Of these three conditions, fact checkers will usually be able to verify only the first. Both knowledge and intention are psychological characteristics and, unless the liar happens to confess both5, a fact checker will be unable to know they hold.

With this understanding of what lies are, let's examine a recent fact check by PolitiFact. I don't mean to pick on PolitiFact here, and I could just as easily have chosen an example from The Post's Fact Checker. I chose the following example simply because it was the first recent one that I discovered that seemed good for making my point. For the purposes of this example, I'll assume that the fact check is itself factually correct.

As mentioned above, the lowest rating on the "Truth-O-Meter" is "Pants on Fire!"; here's how PolitiFact defines that rating: "The statement is not accurate and makes a ridiculous claim.2" One obvious problem with this definition is that what counts as "ridiculous" is a subjective judgment.

The following recent claim was rated "Pants on Fire!": "'It cost the university [of Wisconsin-Madison] $50k (your tax dollars) to remove' a rock considered by some a symbol of racism.6" In this case, someone made the supposedly ridiculous claim that a large rock was removed from a university campus at taxpayers' expense. According to the fact check itself, only one thing in the claim is false, namely, that the money spent to remove the rock came from taxes. Instead, the money came from private donations.

This rates a "Pants on Fire!"? Where is the evidence that the woman who made the claim was lying? What is the evidence that the claim itself was ridiculous?

The University of Wisconsin at Madison is a state university, so the natural assumption would be that the money spent to remove the rock would come from state taxes. According to PolitiFact, this was not true, but it's certainly not a ridiculous assumption to make. The article that the woman who made the claim linked to stated that the money had been privately donated, but she may not have read it before linking to it. If so, that may well be an embarrassing mistake but is it "ridiculous"? Is it ridiculous enough to justify accusing her of lying?

The very fact that the article that the woman herself linked to stated that the money was not from taxes is evidence that this was a mistake and not a lie. Why would a liar link to an article that would immediately reveal the claim to be false? This is not the action of a liar, but of a person who failed to do due diligence in checking the claim herself.

In politics, the "liar, liar" accusation is often thrown around recklessly. Because such an accusation carries a strong moral condemnation, a false accusation poisons the well of discourse, angering those falsely charged and inciting counter-accusations. Fact checkers should refrain from contributing to this already poisonous atmosphere.

Professional fact checkers such as those mentioned above usually do a good job of separating truths from falsehoods, but they are not lie detectors. Lying is morally wrong, but it's not the only thing that is wrong. It's also wrong to make false accusations against innocent people, even when those charges are made in a childish, unserious way. Fact checkers should stop doing so.

Reader Response (8/30/2021): David Hawkins emailed to take issue with the example used in the above entry. David's critique is lengthy, so I'll interject my replies where appropriate:

Rachel Campos-Duffy (RCD) is telling a lie.


A1. Telling a falsehood.
A2. Knowledge of falsity.
A3. Intent to deceive.

Next we are given the "Truth-O-Meter" definition for lying, i.e., the "Pants on Fire" rating; and I agree that compared to the traditional conditions this is inadequate.

B1. The statement is untruthful or otherwise not accurate
B2. The statement makes a ridiculous claim.

From those definitions you conclude RCD did not lie.

No, I didn't conclude that she did not lie; I presumed it. I didn't discuss this above, but there should be a moral presumption of innocence just as there is a legal presumption. Thus, I start from the presumption that RCD did not lie, though that presumption can be rebutted by sufficient evidence. The burden of proof is on PolitiFact to rebut that presumption, and I claim that it failed to do so. In fact, it didn't even try.

I trust these summarize your argument.

C1. Condition A2 is not satisfied because the claim was a mistake and therefore not a lie.

Again, I presume that it was a mistake until the burden of proof is met to show that it wasn't.

C2. Condition A2 is not satisfied because knowledge of falsity is unknowable unless the liar confirms that is the case.
C3. Condition A3 is not satisfied because intent to deceive is unknowable unless the liar confirms that is the case.

I don't claim that those are the only ways to verify those conditions, though admissions are certainly the strongest evidence. For instance, if we knew that RCD had read the article she linked to, that would probably be sufficient evidence of knowledge.

C4. Condition B2 is not satisfied because ridiculousness is subjective.
C5. Condition B2 is not satisfied because the false claim is a reasonable one to assume.

I have drawn some opposite conclusions:

1. Conditions A1 and B1 are the same and we seem to agree RCD makes a false statement satisfying the condition of telling a falsehood.

I also assumed that and didn't verify that the fact check was correct. The news article on which it was based certainly claimed that the money was privately donated, but news articles are sometimes wrong. However, let's continue on that assumption.

2. Condition A2 is satisfied. While I agree with the definition of this condition, I am forced to conclude, however dimly, RCD knows her claim could be wrong in her assumptions without evidence, regardless of the reasonableness of those assumptions. The article RCD supplies to support her claim clearly states private funds were used.

True, but did she read all the way down to the seventh paragraph? If she failed to do so, then she is certainly to blame for not doing so before making the claim. In addition to telling the truth in most circumstances, there is also a moral requirement of due diligence before making a statement.

This is not a case of being ignorant or being mistaken as shown by the evidence below supporting her intent to deceive in 3, 4, and 5.

3. Condition A3 is satisfied. Lying requires that the person intend that other people believe the untruthful statement to be true. RCD is clearly trying to persuade others that her untruthful claim is true. Why else would a media contributor make an untruthful claim in the face of the reported facts?

She was no doubt intending that her readers believe the claim, as she was neither joking nor play-acting, but if she believed it was true at the time she made it then it was not a lie.

4. Condition B2 is satisfied. I agree that "ridiculous" is not a well defined condition for fact-check rating. However, "ridiculous" means deserving or inviting derision or mockery; absurd. The fact that even if RCD's claim was a mistake, it was made false in light of the very article provided to support it fits the definition, thus making it a ridiculous claim.

I agree that it is ridiculous to link to an article that shows your claim to be untrue, since it certainly invites ridicule. However, PolitiFact is wrong if it thinks that the definition of "lying" includes ridiculousness, and its definition of its "Pants on Fire!" rating is itself ridiculous.

5. This untruthful claim is not a mistake. Additional evidence for intent to deceive comes from the pejorative terms used in the tweet and their alignment to political motivations here cannot be dismissed. RCD puts mocking quotes around the term, racist, in referring to the rock as "this 'racist' rock", and refers to the priorities of the "woke UW Madison Taliban". This clearly moves us from ignorance or error into the realm of polemic sophistry invoking political identity issues; RCD is clearly on a side and is promoting her political agenda, even to the point of blinding herself to contrary evidence.

There's no doubt that she was making a political point but that's no evidence that she was lying. Perhaps you're right that she blinded herself to the contrary evidence, but if so then she was not lying. You might say that she was "lying to herself", but lying to yourself is not a literal lie since it violates both the knowledge and intention-to-deceive-others requirements. Self-deception is wrong, but it's a different wrong than deceit of others.

C1 is a wrong conclusion because there is enough evidence to demonstrate RCD knows the claim is false.

C2 is a wrong conclusion because the evidence the claim is wrong exists in the article supplied to support it.

C3 is a wrong conclusion because there is enough evidence to demonstrate RCD's intent to deceive.

C4 is a wrong conclusion because the claim clearly meets the definition of ridiculous.

C5 is a wrong conclusion because the claim is untrue without supporting evidence and is made despite readily available contrary evidence, a clear indicator of intent to deceive.

According to the necessary and joint conditions for lying and the "Truth-O-Meter" conditions for "Pants on Fire", Rachel Campos-Duffy is lying and her moral character is to blame. First, in this case, she is telling a a barefaced lie. Second, speaking falsely in any matter, lying, equivocating, and any way devising and designing to deceive our neighbour, i.e., bearing false witness, is a moral character flaw. Even if the term, "lie", could not be fairly applied, her moral character flaw persists in the fact she is apparently unapologetic for making a false statement in the continued absence of any acknowledgement, correction, clarification, or withdrawal of the claim. So now her claim is intentionally still out there deceiving others with the same confirmation bias that is open to it and influencing those too lazy to check the facts for themselves.

An at least equally plausible hypothesis is that she failed to read the full article before "tweeting" it, then was too embarrassed by her carelessness to admit making a mistake. I'm not defending her moral character; at best, she's guilty of a reckless error, and then failing to publicly admit it, apologize for it, and correct it.

I agree with the sentiment regarding the care in which fact-checking needs to be done. I just think you picked a bad example.

Good! That's the important point that the example was supposed to illustrate. If you still disagree with the example, I expect that you could find one that you do agree with in PolitiFact's archives.

For the reasons given above, I think you've failed to meet the burden of proof to establish that the example was a lie. Specifically, you've been unable to show that either, let alone both, the knowledge and intent-to-deceive-others conditions hold. These, of course, are the difficult conditions to meet, and the ones usually ignored in political accusations of lying.

In politics, the accusation of "Liar, liar, pants on fire!" usually just means that the accuser disagrees with the accused. This is a moralizing, polarizing, and unproductive way of expressing disagreement.

Unlike you, PolitiFact did not even attempt to support its accusation with evidence of knowledge or intent to deceive others. Moreover, its definition of the "Pants on Fire!" rating substitutes a subjective judgment for these requirements, which is ripe for abuse. PolitiFact's fact-checkers are likely to find political opinions that they disagree with ridiculous, and those that they agree with not so, which is a ridiculous way to check facts.


  1. See:
    1. Why You Need to be Able to Check Facts, 9/8/2020
    2. Fact-checking Vs. Nit-picking, 10/20/2020
    3. Four Types of Misleading Quote, 11/27/2020
    4. News Sources Vs. Familiar Quotations, 12/4/2020
    5. Rules of Thumb, 1/2/2021
    6. A Case Study, 2/4/2021
    7. Reliable Sources, 3/2/2021
    8. What is a fact?, 3/2/2021
    9. Sources for Fact-Checking: Primary, Secondary & Tertiary, 5/6/2021
  2. See: "The Principles of the Truth-O-Meter: PolitiFactís methodology for independent fact-checking", PolitiFact, 10/27/2020.
  3. See: Glenn Kessler, "About The Fact Checker", The Washington Post, 1/1/2017.
  4. There's a subtle philosophical issue as to whether lying requires knowledge, or whether mere belief is enough. For my purposes here, it isn't necessary to answer this question.
  5. For an example of a rare case in which all three components were established, see: Debate Doublespeak, 4/19/2008.
  6. Laura Schulte, "No, taxpayer funds were not used to remove rock deemed by some to be racist from UW-Madison campus", PolitiFact, 8/14/2021.

August 23rd, 2021 (Permalink)

Book Review: The Gray Lady Winked

Quote: For decades, the New York Times proudly wore the moniker of the "Gray Lady" because that adjective, gray, spoke to a concrete objectivity, a kind of neutral take on the facts that testified to the bloodless accuracy of its reporting. But as this book shows, for at least the past century, that has not been the case. On many of the most important subjects of the day, the New York Times was neither disinterested nor dispassionate. In fact, as these pages attest, the paper staked a very definite position when it came to its coverage of major historical episodes. My own view is that it's time for us to think differently about the concept of grayness in news reporting. Instead of understanding journalism as either a collection of neutral entities who process unassailable fact into truth or as partisan operators hacking away at an agenda, we should see the endeavor as encompassing a spectrum of ideas and opinions that approximate or come as close as possible to the truth. … This doesn't mean there is no objective truth. I firmly believe there is. But just like in science, journalism done right attempts to come as close as possible to the truth while fully recognizing that it will never present a perfect picture.1

Title: The Gray Lady Winked

Comment: I've read this book and I still don't know what the title means2.

Subtitle: How The New York Times's Misreporting, Distortions & Fabrications Radically Alter History

Author: Ashley Rindsberg

Date: 2021

Summary: This book is a history of some of the The New York Times (NYT)'s crimes against journalism. It consists of ten chapters recounting various incidents in the NYT's misreporting of important historical events of the last hundred years. The chapters range from the 1920s to the present and include such topics as: the 1936 Berlin olympics and Germany's subsequent invasion of Poland that started World War 2; the Holocaust; the early history of the Soviet Union, including the Ukrainian famine of 1932-33; the Cuban revolution; the Vietnam war; the Muhammad Al-Dura affair; the Jayson Blair scandal; the invasion of Iraq; and, finally, the 1619 Project.

Review: I found all of the above chapters individually interesting, though of course some more so than others. Generally speaking, the chapters are independent of one another and could be read in any order, or some skipped without great harm. They are not in exact temporal order, though the first chapter deals with events in the 1920s, and the last with ones from the most recent couple of years.

In the headline to one of his columns as Public Editor of the NYT, Daniel Okrent asked the question: "Is The New York Times a liberal newspaper?3" He answered his own question in the first paragraph of the column: "Of course it is." That's the only motif that runs rather consistently through this history of bad journalism, with most of the chapters being variations on this theme. When the paper makes mistakes, they usually benefit the left.

In reading this book, however, one should not suppose that all this history shows some essential characteristic of the NYT that explains the way the paper is today: that would commit a genetic fallacy. The reason that the NYT is a left-leaning newspaper is some function of its ownership by the Ochs-Sulzberger family, and the fact that it's a metropolitan paper with a predominantly left-leaning readership.

Except for the final chapter on the events of last year, most of this history tells us little about the current state of the NYT. For instance, everyone alive at the time Walter Duranty was misreporting on the Ukrainian famine from Moscow is dead or retired, so that there will have been a complete changeover of personnel at the paper. I doubt that the current NYT would be recognizable to those from twenty years ago, let alone a century. If you want to understand the NYT as it currently is, go straight to the chapter on the 1619 Project.

My only substantive criticism of the book concerns its treatment of the Jayson Blair scandal, which ties in to the NYT's general left-wing bias. Rindsberg only mentions in passing that Blair, who fabricated many news articles, won a minority internship at the NYT. Of course, this wouldn't be a problem except that Blair's minority status played an important role in there being a scandal at all. Throughout his checkered career, Blair was both protected and promoted rapidly in the name of "diversity", despite repeated warnings. The NYT's own article on the scandal comments:

…[V]arious editors and reporters expressed misgivings about Mr. Blair's reporting skills, maturity and behavior during his five-year journey from raw intern to reporter on national news events. Their warnings centered mostly on the errors in his articles. His mistakes became so routine, his behavior so unprofessional, that by April 2002, Jonathan Landman, the metropolitan editor, dashed off a two-sentence e-mail message to newsroom administrators that read: "We have to stop Jayson from writing for the Times. Right now."4

Why was this warning ignored? The Gray Lady Winked doesn't tell you, but William McGowan's book of more than ten years ago, Gray Lady Down, does:

Touching on the combustible issue of racial preferences as a factor in Blair's rise, the [NYT's] report explained that he had joined the Times through a minority-only internship and then was promoted to full-time reporter in January 2001, and that his immediate supervisor, Jonathan Landman, the Metro editor, objected but ultimately deferred to the paper's "commitment to diversity." Landman did warn his higher-ups that editors had to "stop Jayson from writing for the Times," but that memo had little effect. Although the Times denied any connection between Blair and the broader issue of affirmative action, such a conclusion was hard to get around. The recently retired Times columnist William Safire said, "Apparently, this 27-year-old was given too many second chances by editors eager for this ambitious black journalist to succeed." …

To the surprise of many, [editor Howell] Raines admitted that Blair had been a beneficiary of racial favoritism. "Where I come from, when it comes to principles on race, you have to pick a ditch to die in," Raines intoned in his best Southern drawl. "And let it come rough or smooth, you'll find me in the trenches for justice. Does that mean I personally favored Jayson? Not consciously," he continued. "But you have a right to ask if I, as a white man from Alabama with those convictions, gave him one chance too many…. When I look into my heart for the truth of that, the answer is yes."5

Raines and others were doing Blair no favor by turning a blind eye to his misdeeds, and they certainly weren't doing the NYT a favor. If Blair had been punished early for his transgressions, he might have learned not to confabulate. Instead, he got away with it for years, and then when he was finally caught it destroyed his career. The Blair scandal is not an exception to the general rule that the NYT's crimes against journalism are motivated by its left-wing politics. There is a line, albeit a crooked one, from Jayson Blair to the 1619 Project.

Fact-Checking: The only chapters in this book that I knew much about in advance were those dealing with Walter Duranty, the Cuban revolution, and the Jayson Blair scandal. The only simple factual error that I noticed is the claim that Duranty's Pulitzer prize was for his reporting on the Ukrainian famine6, which is a natural mistake to make, but the prize was for his equally mendacious reporting on the Five-Year Plan of a couple of years earlier7. While I suspect that there are other factual errors in the book that I didn't notice or know about, this is an excellent record for a book filled with so much history.

Editing: This book appears to have been published by the author, but the copy-editing is as good as or even better than that coming from professional publishers nowadays. I found only about a half-dozen misspellings, and a few more grammatical errors. So, the book is very well edited, especially by contemporary, admittedly low, standards.

One misspelling I did notice, which occurs twice in the book, is that of "solider" instead of "soldier"8. I've seen this mistake before, and it's one of those that a spellchecking program won't catch because "solider" is apparently a genuine if unusual English word.

While generally well and clearly written, the book could have benefitted from a more thorough edit. Rindsberg is a good writer, but has a tendency to wordiness and repetitiveness. A judicious snip-snip here and there would have improved the readability of the book, and shortened it a little. A few of the chapters I found a little tedious for this reason.

General Comments: If you don't know much about the history of the NYT, you may be surprised or even shocked to find out the truth. Before reading this book, I was aware of some of the cases chronicled here, and for the most part I was sufficiently disillusioned not to be shocked. The biggest surprise for me came in the very first chapter about the NYT's sympathetic pre-war reporting of Hitler's Germany. That was news to me.

As engrossing as I found this history to be, it's questionable how much it has to do with the current state of the paper. The chapter on the 1619 Project tells us far more about that state than all of the earlier chapters together.

Recommendation: Recommended to anyone affected by the NYT's reporting, which is certainly all Americans, and probably most of the rest of the world. Especially recommended to those interested in either the history of the NYT, the history of misreporting, or in the pseudo-history of the 1619 Project. Each of the book's chapters is self-contained, so that they can be skipped without losing the thread, not that there's much of a thread to lose. As a result, it's unnecessary to read the whole book―though I'm glad I did.


  1. Pp. 11-12; unattributed page references are to the ebook version of the work reviewed; paragraphing suppressed.
  2. I speculated about what it meant in the following "New Book" entry: Gray Lady Down, 5/21/2021.
  3. Daniel Okrent, "THE PUBLIC EDITOR; Is The New York Times a Liberal Newspaper?", The New York Times, 7/25/2004.
  4. Dan Barry, David Barstow, Jonathan D. Glater, Adam Liptak & Jacques Steinberg, "CORRECTING THE RECORD; Times Reporter Who Resigned Leaves Long Trail of Deception", The New York Times, 5/11/2003.
  5. William McGowan, Gray Lady Down: What the Decline and Fall of the New York Times Means for America (2010), pp. 35-36.
  6. P. 186.
  7. See: "New York Times Statement About 1932 Pulitzer Prize Awarded to Walter Duranty", The New York Times.
  8. Pp. 147 & 167.

August 12th, 2021 (Permalink)

Here We Go Again: Florida's New Record Number of Cases (Updated)

Some journalists think that this summer is a replay of last summer, as witnessed by the following headline:

Florida still breaking records for daily COVID cases;
single-day high reaches 28,3171

We're also back to the dreaded "surge" of last summer, according to the story beneath the headline:

The coronavirus surge in Florida continues with another record-breaking day of new cases reported Monday. Florida's daily case count reported Monday by the Centers for Disease Control and Prevention shows 28,317 new cases for Sunday and 28,316 for Saturday, both significantly higher than the record-breaking case count of 23,908 reported Friday.1

This time we can't blame the news media, at least not entirely, as later reports revealed that the numbers released by the government were false:

The Centers for Disease Control and Prevention (CDC) adjusted a discrepancy with Florida COVID-19 data on Tuesday, though the new numbers still are not the same as those provided by the state. On Monday, the CDC reported the state saw another record number of new COVID cases. But the Florida Department of Health disagreed. On Monday, the Centers for Disease Control and Prevention reported 28,317 new cases in the state. Numbers from Sunday showed 28,316 people tested positive. The Florida Department of Health said those numbers were accumulated over "multiple days" and later provided the following figures:
  • Friday, Aug. 6: 21,500
  • Saturday Aug. 7: 19,567
  • Sunday, Aug. 8: 15,319
  • 3-day average: 18,795

Gov. Ron DeSantis said on Monday that he suspected that, since the CDC does not report on Sundays and Florida sent in three days worth of data, the federal agency combined the numbers.2

This is a puzzling explanation. What does it mean to "combine" the numbers? It can't mean addition, since adding just two of the days produces at least 35K cases, and all three add up to more than 55K. "Combine" also can't be the mean average of all three numbers since, as shown, that average is about 10K less than the number put out by the CDC. Here's a somewhat plausible explanation of how the CDC arrived at the numbers they reported:

One of the state's leading epidemiologists said it appears the federal agency made a simple math error. "It appears the CDC divided by two instead of three," said Jason Salemi, an epidemiologist at the University of South Florida, who runs one of the most comprehensive and closely watched COVID-19 trackers in the state. Instead of spreading the 56,386 cases the state recorded from Friday through Sunday over three days, it spread them over two days, which inflated the one-day tally, he said. The only significance was that Florida didnít set a new one-day record on Sunday for new cases. The record, set on Friday with 21,500 new cases, still stands.3

This explanation doesn't work perfectly, since half of 56,386 is 28,193, which is close to, but not exactly, what the CDC reported. 56,386 is the sum you get if you add up the numbers for Friday through Sunday provided by the FDOH. The explanation does explain one odd thing: I was struck by the fact that the numbers reported by the CDC for Saturday and Sunday differed by only one case―28,317 and 28,316―which could be explained as the result of dividing an odd number of cases by two, then allotting the remainder to one of the two days. If this explanation is correct, then the FDOH must have reported 56,633 cases to the CDC. I guess this could be called "combining" three days worth of cases into two.

The same article that reported the bogus number quoted above also reports that "232 people died from COVID-19 in the last two days1". It was published Monday so that the deaths would have occurred over the weekend. The article reporting the corrections also states:

The CDC reported 28,317 new cases of COVID-19 on Sunday. Along with the over 28,000 cases, 120 deaths were also logged, according to data from the agency.2

So, the 120 would also have been on Sunday. Currently, the CDC reports 21 deaths on Sunday and 17 on Saturday for a total of 383. So, where did the 120 and 232 come from? Are they also false numbers? The article doesn't tell us, and I can't find any indication that the FDOH corrected either of these numbers4.

Two things do seem to be different this summer from last:

  1. The CDC is putting out false data. I don't recall this happening last summer. Last year, it was the news media that reported a series of bogus "records" that were the result of multiple days' worth of statistics being reported as if they all occurred on the same day5. Apparently, something similar happened here, but the CDC was the culprit.
  2. The state department of health is correcting it. I don't remember the Florida Department of Health (FDOH) making any effort last summer to correct the news media's misleading reporting. The correction article quoted above also reports:
    During the first year of the pandemic, the Florida Department of Health released daily COVID-19 case numbers. It switched to weekly numbers recently though, relying on the CDC to track the daily numbers instead.2

    The report doesn't explain why the FDOH made this change, but it may be because of the alarmist reporting of "record highs" last summer. Of course, the FDOH didn't count on the CDC releasing false data.

Update (8/13/2021): Yesterday, as I was writing the above entry, The Texas Tribune published an article with the following claims: "Over 5,800 children in Texas were newly hospitalized with COVID-19 in the seven-day period ending on Aug. 8, according to the Centers for Disease Control and Prevention, a 37% increase from a week prior.7" Later the same day, the article was corrected to the following, which is what you'll read if you look at it today:

From the start of the pandemic through Aug. 9, over 5,800 children in Texas have been hospitalized with COVID-19, according to the Centers for Disease Control and Prevention. There were 783 children admitted to Texas hospitals with COVID-19 between July 1 and Aug. 9.8

In addition, the following notice was added to the top of the article:

Correction, Aug. 12, 2021: An earlier version of this story overstated the number of children who have been hospitalized in Texas recently with COVID-19. The story said over 5,800 children had been hospitalized during a seven-day period in August, according to the Centers for Disease Control and Prevention. That number correctly referred to children hospitalized with COVID-19 since the pandemic began. In actuality, 783 children were admitted to Texas hospitals with COVID-19 between July 1 and Aug. 9 of this year.8

I can't tell from the correction note whether the fault here lies with the CDC or with the reporter, who may have simply misread the CDC's statistics.

Why do these sort of mistakes always exaggerate the effects of the disease? The CDC's mistake about Florida nearly doubled the number of cases on Sunday, the supposed new record high, and the exaggeration in the Texas case is even worse. Notice that even the correction exaggerates by comparing apples to oranges: in the mistake, 5,800 was supposed to be the number of children hospitalized in the first week of this month, whereas the corrected figure of 783 includes the entire month of July.

To make this a fair comparison, let's look at the figures per day: The mistake claimed that over 828 children were admitted per day, whereas the correction has it under twenty. So, the mistake exaggerates the number of children hospitalized by over forty times.

Why do these mistakes always support the story being told by the news media? You seldom see a correction that strengthens an article's claims. Notice that the Texas error is in an article that still bears the headline:

Texas children and children's hospitals are under siege from two viruses: RSV and COVID-192

They're "under siege", just like the Alamo! Of course, 828 children hospitalized a day probably would put Texas hospitals "under siege", but what about only twenty?

Update (8/16/2021): Finally, Florida has changed the way that it reports COVID-19 cases and deaths so that now they are assigned to the day they actually occurred, rather than being released to the press on whatever day the state department of health happened to receive notice of them. As I explained in considerable detail last summer5, the past practice led to a steady series of misleading headlines of "record high deaths". Understandably, such reporting led to political pressure to react in counter-productive ways.

Unsurprisingly, the news media is unhappy that now it will be more difficult for it to create such tabloid headlines. For instance, here's how a Florida newspaper reported the change: "Just as a highly contagious new delta variant sent Florida into a vicious COVID-19 surge, the state Department of Health changed the way it reports cases and deaths attributed to the virus.9" Notice the emotive language: the "surge" is "vicious". Also, notice the juxtaposition: the change was made "just as" the "vicious surge" began, insinuating without evidence that there's some connection between the two.

After seven paragraphs suggesting that there's something wrong with the change, the article finally gets around to describing it: "Florida changed its COVID reporting method Tuesday and now reports when cases or deaths actually occurred rather than when they were communicated to the state―allowing health officials to assign cases or deaths to days in the past rather than the present." What's wrong with that? If the cases or deaths happened in the past, then shouldn't that be where they are assigned, rather than in the present when they didn't happen?

Yet, the article claims in the second paragraph: "The result: Florida no longer provides a real-time picture of how COVID is impacting the state." Not true! How would assigning cases and deaths to the day they occur, rather than when they are reported to the state, mean that the state is no longer providing a "real-time picture" of the progress of the disease? The former reporting system gave a false picture of the disease's progress, marked by waves of cases and deaths that were obviously artifacts of the system. When a backlog of cases was suddenly dumped by local and county health departments onto the state, the news media would jump on it and pronounce it a "record high" number of cases, when it was only a record in the number of cases reported to the state.

The article inadvertently reveals what the news media objects to: "Since Tuesday, Florida continued to revise its information based on the actual dates of cases or deaths, even adjusting some record-breaking daily case counts downward." That very fact reveals that the "records" were not genuine but artificial ones generated by backlogs.

An expert is quoted: "'For Florida to move to a new system of reporting is technically correct, but in actuality, it is problematic because it distorts data,' said Bill Ku, a data scientist and former researcher at Columbia University…". How does a "technically correct" change distort data? If it distorts data then it can't be technically correct. In fact, it's the previous method that distorted data, which had to be corrected later.

My best guess about what Ku may have had in mind is that there will be a lag time in reporting some cases, which means that the last week or two of cases―depending on how long the lag time is―will tend to be under-reported. The article includes a chart that shows the numbers of deaths rising according to the old method, and falling according to the new one. The legend on the chart explains that:

On Aug. 10, Florida revised its reporting method, adjusting the COVID-19 death counts to reflect the actual days when the deaths occurred rather than when they were reported. The lag between a death and the date it was reported creates an artificial appearance that deaths are decreasing.

What it doesn't explain is that the old method inflated the number of deaths by including ones that occurred on earlier days. Both trend lines are potentially deceptive, but it's only the older method that allowed news outlets to hype the latest "record high" deaths for several days in a row.

In the original entry, above, I pointed out that the CDC had originally claimed a total of 232 deaths in Florida over the first full weekend of this month, and 120 on Sunday, whereas they later showed only 17 on Saturday and 21 on Sunday. The CDC is now showing 103 deaths on Saturday and 65 on Sunday the eighth, for a total of 168 over the weekend, which is quite a bit less than what the CDC originally reported but closer. The change is probably due to the lag in reporting. Given that over a week has passed since, these numbers shouldn't change much more.

There is a potential for misunderstanding both ways of reporting cases and deaths, but the news media never bothered to explain the problem with the previous method, presumably because there was never an incentive to do so. Now there is.

By the way, this article is by the same journalist who reported the false CDC numbers discussed in the original entry, above. In that case, it was the CDC that was at fault for spreading incorrect numbers. In this case, it's the reporter's fault.

Update (9/3/2021): Never underestimate the ability of the major news media to find a way to hype the coronavirus. As I explained in the previous update, the FDOH changed the way it reports cases and deaths in order to assign them to the days they happened, rather than when the agency received the report.

I don't know, but certainly suspect, that the reason for this change was to discourage the alarmist reporting of "record high" cases or deaths due to backlogs being reported all at once. However, the Miami Herald has found a way around the change, so that they can still post tabloid headlines such as the following:

Florida COVID update: 901 added deaths, largest single-day increase in pandemic history10

The headline gives the impression that the 901 deaths all occurred on a "single-day", but that's not true. In a typical bait-and-switch tabloid move in which the article takes back what the headline gives, the second paragraph of the article explains:

All but two of the newly reported deaths occurred after July 25, with about 78% of those people dying in the past two weeks, according to Herald calculations of data published by the CDC. The majority of deaths happened during Florida's latest surge in COVID-19 cases, fueled by the delta variant. It is the largest single-day increase to the death total in the state's COVID pandemic history.10

So, only about three-fourths of those 901 deaths occurred over the preceding fortnight, let alone on a single day! Of course, some people will read just the headline and end up believing that 901 deaths happened in one day. This is not speculation, as people have "tweeted" such "tweets" as the following: "901 died in Florida yesterday because of covid", "Well 901 died yesterday in Florida, some beds emptied", and "More people died of Covid in Florida yesterday (901) than in the terrorist attack at Kabul airport11." The Herald should now be on notice that these sort of headlines mislead people, and if such headlines continue, we'll have every right to assume that it is misleading them intentionally.

Where did the paper get this number? What it did was to reverse engineer the statistics that the FDOH sent to the CDC. The paper included the following explanation of what it did in a separate "Behind Our Reporting" section that probably won't be read by many:

The Herald publishes the number of new COVID-19 cases and deaths reported by the Centers for Disease Control and Prevention after each update by the agency. On Aug. 10, the Florida Department of Health changed the way it reported new cases and deaths to the CDC. Cases and deaths used to be logged as total new cases reported on a single day. Now, Florida is reporting cases by the "case date," according to the CDC, rather than the date the case was logged into the system. The result of this change is a lag in cases by date and a number of cases back-filling over time.10

As I mentioned in the original entry, above, the FDOH is fighting back against such misleading reporting, in this case putting out the following statement:

As many epidemiologists and informed health professionals would know, there is an inherent lag when deaths are reported to the Department from external sources. That is why relying on date of death, rather than date reported, is the most accurate representation of COVID-19 trends and surveillance.12

So, if the single-day record for deaths due to COVID-19 in Florida is not 901, what is it and when did it happen? The current record is 263 on the fourteenth of last month, which is less than a third of what the paper reported13.

Despite criticism, the newspaper is undeterred: "The Herald will continue to report the difference in total cases and deaths from one day to the next in stories about daily new cases and deaths, as this is consistent with the way data have been presented in daily stories since the beginning of the pandemic." So, its justification for continuing to mislead its readers is that this is the way it's been misleading them since last year. But it's consistent!


  1. Cindy Krischer Goodman, "Florida still breaking records for daily COVID cases; single-day high reaches 28,317", South Florida Sun Sentinel, 8/9/2021. This false news is still available uncorrected from Yahoo News, but the South Florida Sun Sentinel seems to have scrubbed it from their website.
  2. Dale Greenstein & Rachael Krause, "CDC adjusts Florida COVID case numbers after discrepancy Monday", Bay News 9, 8/11/2021.
  3. Jane Musgrave, "Florida accuses CDC of inflating COVID numbers in apparent CDC mistake", The Palm Beach Post, 8/10/2021.
  4. I've emailed the FDOH with a query but haven't received a reply yet. I'll update this entry if and when I do.
  5. Florida's Record-High Death Tolls, 8/12/2020.
  6. "Trends in Number of COVID-19 Cases and Deaths in the US Reported to CDC, by State/Territory", The Centers for Disease Control and Prevention, accessed: 8/12/2021; see under "Florida" and "Daily Deaths".
  7. Reese Oxner, "Texas children and children's hospitals are under siege from two viruses: RSV and COVID-19", The Texas Tribune, 8/12/2021. This is the Internet Archive Wayback Machine's capture of the original article. As explained above, the current version of the article has been corrected.
  8. Reese Oxner, "Texas children and children's hospitals are under siege from two viruses: RSV and COVID-19", The Texas Tribune, 8/12/2021. This is the current, corrected version of the article.
  9. Cindy Krischer Goodman, "Florida no longer provides a real-time picture of how COVID is impacting the state", South Florida Sun Sentinel, 8/16/2021. All subsequent quotes are from this article.
  10. Devoun Cetoute, "Florida COVID update: 901 added deaths, largest single-day increase in pandemic history", Miami Herald, 8/27/2021. Paragraphing suppressed.
  11. Sarah D., "Miami Herald reporter attempts―and fails―to defend article featuring deliberately misleading headline on Florida COVID19 deaths", Twitchy, 8/27/2021.
  12. "Florida Department of Health Sets the Record Straight on False Data Claims by the Miami Herald", Florida Department of Health, 8/31/2021.
  13. "Trends in Number of COVID-19 Cases and Deaths in the US Reported to CDC, by State/Territory", Centers for Disease Control and Prevention, accessed: 9/3/2021.

August 10th, 2021 (Revised: 8/11/20216) (Permalink)

Think Twice Before Splitting an Infinitive

Many of today's linguists are would-be icon smashers. They see their job as pulling down the statues honoring alleged rules of grammar or word meaning. A favorite target of their wrath is the alleged grammatical rule against splitting infinitives. I write "alleged" because I was never taught such a rule, and I'm no youngster. If there ever was such a rule, it's been dead for longer than most of us have been alive. Though the linguists see themselves as iconoclasts fighting a stodgy establishment, they are the defenders of the current conventional wisdom.

The bogeywoman of these linguists is an elderly schoolmarm, her greying hair tied up in a tight bun at the back of her head, rapping her students' knuckles with a ruler whenever they split an infinitive. We even know her name: Miss Bertha Thistlebottom1. Thankfully, I never learned grammar in Miss Thistlebottom's class, but then I was never taught grammar at all as far as I can remember. In high school, I didn't know an adjective from an adage. Instead, I had to teach myself grammar long after "grammar" school, no thanks to the linguists.

In addition to Thistlebottom, the favorite whipping boys of such linguists are William Strunk, Jr. and E. B. White, authors of The Elements of Style. Unlike Thistlebottom, they were both real people, but are now as dead as the rule against splitting infinitives. Their little book is loathed in a way that is hard to explain except as a result of jealousy at its surprising and continuing success. So, what do Strunk & White have to say about splitting infinitives? Surely, like Miss Thistlebottom, they condemn it as an illiterate grammatical error?

No such thing. Here's everything that S&W had to say about the subject in the first edition of the Elements, published in 1959:

There is precedent from the fourteenth century downward for interposing an adverb between to and the infinitive it governs, but the construction is for the most part avoided by the careful writer. …

The split infinitive is another trick of rhetoric in which the ear must be quicker than the handbook. Some infinitives seem to improve on being split, just as a stick of round stovewood does. "I cannot bring myself to really like the fellow." The sentence is relaxed, the meaning is clear, the violation is harmless and scarcely perceptible. Put the other way, the sentence becomes stiff, needlessly formal. A matter of ear.2

What rigid traditionalists!

Despite inveighing against our latitudinarian linguists, above, albeit with tongue in cheek, I have no intention of defending Miss Thistlebottom. There is no grammatical rule against splitting English infinitives―what's more, there never was. However, it's a good linguistic rule of thumb to avoid it, as S&W suggest.

S&W don't explain why the "careful writer" should avoid splitting infinitives, but here's one reason: split infinitives can be ambiguous, and the careful writer, or speaker, avoids ambiguity3. To see why this is so, let's examine the most famous split infinitive of them all, from the narration at the beginning of the original 1960s Star Trek television series:

These are the voyages of the starship Enterprise. It's five-year mission: … To boldly go where no man has gone before!4

There are two possible ways to avoid splitting the infinitive "to go" with the adverb "boldly" in the final phrase:

  1. To go boldly where no man has gone before!

    Here, the adverb modifies the verb that it is next to, that is, "boldly" modifies "go", which we can indicate this way: To [go boldly] where no man has gone before. "Boldly" is thus an adverb of manner that tells us in what manner―namely, with boldness―to go where no man has gone before.

  2. Boldly to go where no man has gone before!

    This alternative may sound rather unnatural, but you can get used to it. The adverb is separated by "to" from the verb, so it modifies the entire remainder of the phrase, which we can indicate as follows: Boldly [to go where no man has gone before]. In other words, going where no man has gone before is a bold thing to do.

So, these two phrases do not mean the same thing. In the first, it is the manner of doing the action that is bold; whereas, in the second, it is the action itself that is bold. That these are not the same thing can perhaps be seen more clearly in a different example: "To go through the door". "Boldly to go through the door" would mean that the act of going through the door itself was bold. Suppose that one knew that there was a sleeping tiger on the other side of the door, then the very act of going through the door would be bold. In contrast, "to go boldly through the door" does not mean that simply going through the door is itself bold, but that the door is entered in a bold way, say, by throwing it open and striding rapidly through.

Which of these two possible meanings were intended by Gene Roddenberry4? By splitting the infinitive, the adverb can be interpreted in either way. Was the Enterprise supposed to go where no man has gone before in a bold manner, say, zooming into other star systems at warp speed, not raising shields, and so on? Or, is it that the very mission of going where no man has gone before is a bold one, which certainly sounds true?

With these distinctions in mind, we can see that it's possible to meaningfully say: "Boldly to go cautiously where no man has gone before", though that doesn't mean you should do so. It may sound like an oxymoron, but needn't be so interpreted. The first adverb, "Boldly", means that going where no man has gone before is a bold thing to do, while the second, "cautiously", describes the manner in which that bold thing is done. So, "boldly to go cautiously through the door" would mean that going cautiously through the door was a bold thing to do, since there is a sleeping tiger on the other side. Doing so cautiously would mean something like opening the door slowly, and sidling through quietly in order not to awaken the tiger. Though it's possible to make sense of infinitives that are modified by two adverbs in this way, I wouldn't recommend forcing your audience to do so.

Now, sometimes the careful writer wants to be ambiguous. Did Gene Roddenberry, who apparently added the split infinitive to the opening narration for Star Trek4, intend it to be ambiguous between 1 and 2, above? Did he want to boldly split infinitives that no man had dared to split before? I don't know, but I do know that a careful writer should be aware of the potential for ambiguity in doing so.

However, sometimes you may need to split an infinitive in order to avoid ambiguity. For instance, consider the sentence:

The difficulty in assessing his achievements is that he tries to absurdly exaggerate them5.

Here, the infinitive "to exaggerate" is split by the adverb "absurdly". So, let's move it before "to":

The difficulty in assessing his achievements is that he tries absurdly to exaggerate them.

Now it's ambiguous as to whether the adverb modifies "tries" or the infinitive: is it the trying that is absurd or the exaggeration? Putting the adverb directly after the infinitive sounds absurd, but it could be placed at the end of the sentence:

The difficulty in assessing his achievements is that he tries to exaggerate them absurdly.

This places the adverb as far away from the infinitive it modifies as possible, which is generally not good practice, but at least it makes sense. So, unless we put the adverb all the way at the end of the sentence, the only way to avoid ambiguity is to split the infinitive. I'll let you judge which is better.

Does this mean that you're damned if you split and damned if you don't? No, rather, it means no simple rule governs whether to split an infinitive. The careful writer has to be a careful thinker, keeping in mind that both splitting and not splitting can lead to ambiguity.

So, your future mission is: boldly to split infinitives cautiously.


  1. See: Theodore M. Bernstein, Miss Thistlebottom's Hobgoblins: The Careful Writer's Guide to the Taboos, Bugbears and Outmoded Rules of English Usage (1984). Despite its tilting at a straw woman in its title, this is a sensible usage guide, and more entertainingly written than most such books. Bernstein was not a linguist but a New York Times editor.
  2. William Strunk, Jr. & E. B. White, The Elements of Style (1959), pp. 46 & 64. Strunk, in the original version of the book published in 1918 before White revised it, and presumably when Miss Thistlebottom still ruled the classroom, wrote not one word about split infinitives. See: The Elements of Style (1918).
  3. I learned about this type of ambiguity from philosopher and logician Michael Dummett's book: Grammar & Style for Examination Candidates and Others (1993), p. 79.
  4. Caroline Cubé, "To Boldly Go: the Hurried Evolution of Star Trek's Opening Narration", UCLA Library, 10/11/2016.
  5. See: H. W. Fowler, A Dictionary of Modern English Usage (2nd edition, 1965), under "split infinitive". The example is based on a real one quoted by Fowler. Dummett also mentions this type of ambiguity; see p. 78.
  6. I revised this to clarify the Star Trek example, to add a disambiguation of the Fowler/Dummett example that occurred to me after the entry was posted, and to make some stylistic improvements.

August 4th, 2021 (Permalink)

The Return of Three-Dice Monty

"Step right up, ladies and gentlemen, and try your luck," Monty* bellowed to the crowd passing his midway booth. "As a blind man could plainly see if he had eyes, I have here three fair and unloaded dice." He waved his hand at a strange contraption that was attached to the top of the counter at the front of his booth: it was an hourglass-shaped cage, hinged at the narrow middle part with a handle sticking out towards Monty. In the lower section of the cage, sitting on its bottom, were three large dice.

A few members of the crowd stopped and drifted over to Monty's booth. "When I turn this here handle," Monty continued, at a lower decibel level, "the dice tumble together, and then when I stop turning it, the dice fall to the bottom." Monty cranked the handle a few times and the cage rotated, the dice rattling around inside, then finally coming to rest at the bottom again.

"Now, here's what I'm going to do: you pick a number from one to six. Any number you choose! You bet a dollar on that number. I will give these dice a tumble and if your lucky number comes up once," he said, holding up his forefinger, "you win a dollar. If your number comes up twice," he held up two fingers, "you win two dollars. And if your number comes up thrice," and he held up three fingers, "you win three dollars!

"Now, there's a one in six chance of your chosen number coming up on a single die," Monty continued. "Given that what comes up on any one of these dice doesn't affect the others, that would mean the chance of your number coming up is one-sixth plus one-sixth plus one-sixth, which adds up to one-half! If your number don't come up, then you lose a buck; but if it does, you win at least one. If that ain't a fair bet, what is it?

"What's more, if your lucky number comes up twice, you win double! If it comes up three times, you win triple! How can you lose? Now, put your money down right here on your favorite number!"

Should you bet on Monty's dice game? Is it a fair bet? Are the odds really in your favor or in Monty's?

Extra Credit: How much does a player stand to win or lose in the long run?

* In case you haven't met Monty before: he's a trickster who always speaks the truth and nothing but the truth, but he doesn't always tell the whole truth. Moreover, he disdains the use of sleight-of-hand or gimmicks, using sleight-of-mind, instead. For previous puzzles involving Monty, see:

August 2nd, 2021 (Permalink)

Flaunt or Flout

Another common confusion that your spell-checking program won't catch1 is that between "flaunt" and "flout". The spelling and pronunciation of these two words is similar, which contributes to their confusion, but their meanings are very different. Both are transitive verbs, so that even a grammar-checking program probably won't stop you from confusing them. "To flaunt" means to show something off, especially in a flamboyant or offensive manner2; whereas, "to flout" means to intentionally and openly break a rule3. As with the use of "perpetuate" when what is meant is "perpetrate"4, this mistake seems to go only one way: "flaunt" is written when "flout" is meant.

Almost all of the usage books that I've checked warn against this confusion5, so it appears to be surprisingly common. I've noticed it myself previously, but was recently reminded of it by the following passage from a book:

"Under any definition, the Defendant has flaunted the system," [Judge] Lester wrote. In that "flaunt" means "show something off" Zimmerman "flaunted" the system under no known definition―Lester meant "flout"….6

Don't flaunt your ignorance by flouting the distinction between these two words.


  1. For previous entries in this series, see:
  2. "Flaunt", Cambridge Dictionary, accessed: 8/2/2021.
  3. "Flout", Cambridge Dictionary, accessed: 8/2/2021. An older meaning of "to flout" was "to mock or scorn", which is the meaning found in Shakespeare. The modern meaning contains a remnant of this old meaning in that to flout a rule means to break it in a flagrant way that shows disdain for it.
  4. See: Perpetrate or Perpetuate, 7/2/2021.
  5. One odd exception is Strunk & White, who do not mention it in their chapter on commonly misused words and expressions, see: William Strunk, Jr. & E. B. White, The Elements of Style (4th edition, 1999), ch. 4.
  6. Jack Cashill, 'If I Had a Son': Race, Guns, and the Railroading of George Zimmerman (2013), p. 144.

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