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May 30th, 2021 (Permalink)

A Meeting of the New Logicians' Club

As you may recall from previous visits to the Logicians' Club*, that club's membership was formerly limited to perfect logicians. Since very few logicians are perfect, the membership was quite small, never exceeding single digits. I, for instance, was not a member, as I made a mistake on the entrance test. Given its small membership and, accordingly, small treasury, the Club has decided to drop the requirement of perfection and admit any logician who wishes to belong. As a result of its weakened entrance qualifications, the club's membership has burgeoned. Now, instead of meeting at a small table in a tavern, the club gathers in a meeting room at a hotel.

I visited the Club at its most recent meeting as a guest to see whether it would be worth joining. The evening I attended, the members were playing a game: as each member arrived for the meeting, a coin would be flipped. If the coin came up heads, the member would answer every question truthfully for the entire evening; if it came up tails, the member would lie in answer to any question. Each member of the club knew the truth-telling status of every other member. As a non-member, I was not part of the game and didn't know who was a truth-teller and who a liar.

I wanted to ask the President of the club some questions about the organization, but he was also a member and, therefore, a truth-teller or a liar. Would he answer truthfully or lie? At first, I thought that I would just ask him outright whether he was a truth-teller or a liar, but then I realized that if he was the former he would truthfully answer the question affirmatively, and if he was the latter he would answer falsely the same way. So, that was no way to find out whether I was talking to a truth-teller or a liar, which was also true of any other club member.

When the President called the meeting to order, all of the present members sat down around a large round table that sat in the middle of the meeting room. As a non-member I was left standing and watching. Since asking members directly whether they were truth-tellers or liars wouldn't work, I thought of asking them about other members. So, I asked the President, who was seated closest to me, whether the next member clockwise around the table was a truth-teller or a liar. A liar, he answered.

Intrigued, I asked that member the same question about the next member to the left. Again, the answer came back: a liar. So, I proceeded seat-by-seat, member-by-member around the table, asking each the same question. Always the same answer came back. Finally, I arrived back where I started and asked the question of the member seated to the right of the President. The President was a liar, I was told. So, I decided not to join the club because they're all a bunch of liars! Just kidding.

Now, I have a question for you: Was the number of members of the club seated around the table even or odd?

If you can not only answer this question correctly―there's a fifty-fifty chance of guessing right―but understand the reason for the answer, you are definitely New Logicians' Club material. When you think you've got the answer, click on the "Solution" button below, and all will be revealed.

* For meetings of the old Logicians' Club, which was not a club for old logicians―though some of its members were elderly―but the club limited to perfect logicians, see:

May 25th, 2021 (Permalink)

Q&A: Too Many Fallacy Lists

Q: Reading all the websites on logical fallacies, including Wikipedia, I've been left wondering if there's actually one "exhaustive" and "authoritative" list of all logical fallacies in existence, or whether they have essentially infinite variations and one can only categorize them in broad but finite categories and go from there? It just looks like everyone has their own set of fallacies and it's not clear why that particular set was chosen and not the other. Hope you can clarify that.―Zakhar

A: One reason why there are so many different lists of logical fallacies, and no one authoritative and comprehensive list, is that different list compilers use different definitions of "logical fallacy". So, while such lists may appear to be listing the same thing, they're really not.

For instance, I define "logical fallacy" as "a common type of misleading error in reasoning". There really are an infinite number of possible errors in reasoning, so that listing them all would be a hopeless task.

A useful analogy is between reasoning and traveling: think of making a cross-country trip from point A to point B. There are an infinite number of points other than the destination B that you could wind up at, but there are a finite number of mistakes that you are likely to make during the trip, such as wrong turns. In this analogy, a logical argument is like an attempted voyage from its premisses to its conclusion, and logical fallacies are warning signs along the road that read "Wrong Way" or "Dead End".

So, the definition is not trying to accomplish the impossible task of capturing every particular mistake that someone could make in reasoning, but only types of error. Thankfully for logicians, logical errors tend to follow certain common patterns, so they can be group together in categories by similarity. It's possible to group an infinite number of entities into a finite number of categories; for instance, we group the natural numbers into the two categories of even and odd.

There are two additional parts to my definition that rule out certain so-called fallacies that may be found in other lists1:

  1. Commonness: To be worth listing, a type of logical error should be common, that is, there should be numerous members of its type. Some other lists do not take uncommonness into account. Logical fallacies should serve as a warning to people not to make this kind of error or be taken in by it, and it's not worth warning people about extremely rare but possible threats, such as being hit in the head by a meteorite. Some traditional fallacies are no longer common, such as Aristotle's fallacy of Accent, but I include it because people may have heard of it and wonder what it means.
  2. Misleadingness: A type of logical error should be at least potentially misleading to be worth listing. If the error is obvious and would be unlikely to fool anyone, then it isn't a threat worth warning people about. This is one reason why The Fallacy Files does not include non sequitur as a fallacy, though other lists do, since a non sequitur is an obvious mistake in reasoning2.

I think that it's at least theoretically possible that every logical fallacy―according to my definition―could be listed, but I don't claim to have accomplished that task.

All of that said, there is more overlap between different lists of logical fallacies than may be apparent at a glance. There are multiple names for many fallacies; for instance, "False Dichotomy", and "The Either/Or Fallacy" are both names for the same fallacy. So, if you see two lists of fallacies, one of which includes "False Dilemma" and the other has "Bifurcation", these are probably the fallacy that I prefer to call "The Black-or-White Fallacy". At least some of the apparent differences in the lists may be due to differences in fallacy names, rather than differences in the meaning of "fallacy".

I hope this clarifies at least a little what is a complicated issue.


  1. I include some fallacies in the list because they are traditional―notably, argumentum ad baculum―and not because they meet my definition. "Ad baculum" is not really a type of error in reasoning, but an abandonment of reason for violence or the threat of it. See the entry available from the drop-down list to your left.
  2. For more on why non sequitur is not a fallacy, see: Q&A, 11/9/2007.

New Book
May 21st, 2021 (Permalink)

Gray Lady Down

Quote: "For too long, the New York Times has been seen as the sole (or at least the primary) arbiter of truth in journalism. It lost sight of the clichéd but very effective idea that journalism is the 'rough draft' of history and instead strove to present the crystallized final version. Large swaths of the American public, and in particular the country's elite, certainly believed this to be the case (or, at least, they acted as if it were). The New York Times was not scrutinized the way any institution that serves a critical public function ought to be. No one was watching the watchdog."1

Title: The Gray Lady Winked

Comment: I'm not sure I understand the title of this new book. "Gray Lady" refers to the subject of the book, namely, The New York Times (NYT). It's the word "winked" that puzzles me; I can think of two possible interpretations:

  1. One meaning of "wink" is to close both eyes, as in the idiom "to get forty winks" for a nap. This is the meaning used in Shakespeare's lines from Macbeth:
    Stars, hide your fires;
    Let not light see my black and deep desires:
    The eye wink at the hand; yet let that be,
    Which the eye fears, when it is done, to see.2

    Macbeth wishes for his eyes not to see what his hands do. Perhaps the author of the title is suggesting that the NYT has closed its eyes to what it is doing, or perhaps has metaphorically gone to sleep.

  2. Another meaning of "wink" is, of course, a rapid closing and opening of just one eye. One meaning conveyed by such a wink is that the winker is in on a practical joke, or a shared secret with the winkee. This seems to be the meaning used in the following lines from another Shakespeare play, A Midsummer Night's Dream:
    Ay, do, persever, counterfeit sad looks,
    Make mouths upon me when I turn my back;
    Wink each at other; hold the sweet jest up:
    This sport, well carried, shall be chronicled.3

    In this sense, if the Gray Lady winks, she's sharing a practical joke with us, or indicating that she's not serious.

I can't tell which of these meanings the title author intended, though perhaps it was meant to ambiguously suggest both.

Subtitle: How the New York Times's Misreporting, Distortions and Fabrications Radically Alter History

Comment: I've been criticizing the NYT increasingly of late4, but that's because it's been in a downward spiral for the last several years. I don't suppose that the paper will actually fold, but I'm worried that I'll end up wishing it would. There are, of course, still people there who do excellent work, such as David Leonhardt's reporting on the coronavirus epidemic5, or Ben Smith's on the NYT's "Caliphate" podcast6. However, given the current censorious climate at the paper7, I wonder how long that will last.

Some nitpicks: I'm not sure what the word "radically" is doing in the subtitle; does it mean that the NYT really, really alters history? Wouldn't it be enough to say that it alters history? In addition, "misreporting" seems to cover both "distortions" and "fabrications". I would have preferred: "How the New York Times's Misreporting Alters History".

Author: Ashley Rindsberg

Comment: I'd never heard of Rindsberg before. He has two previous books to his credit―a novel and a collection of short stories―neither of which I've read. So, he appears to be mainly a writer of fiction, which should well qualify him for writing about The New York Times.

Just kidding! This book appears to be primarily a work of history, with only the last chapter dealing with The Times' recent efforts in pseudo-history. According to his brief biography, Rindsberg doesn't appear to be an historian or to have a degree in history. Instead, it says he has a degree in philosophy―presumably a bachelor's degree―which I'm certainly in no position to criticize. Of course, you don't have to have a degree in history to write about history, but it wouldn't hurt. As long as Rindsberg gets the facts right, and doesn't do any distorting or fabricating of his own, it won't matter that he's not specifically trained in history, but how are those of us who are also not so trained supposed to judge whether he's getting it right?

Unfortunately, the book begins with a brief foreword by Mark Crispin Miller, who has a long history of promoting conspiracy theories, including 9/11 ones and the claim that vaccines cause autism8. He also wrote an entire book that I haven't read claiming that the Republicans stole the presidential election in 20049. I hope that the presence of the foreword doesn't indicate that the book is similar claptrap.

Summary: So far, the only parts of the book that I've been able to read are the foreword, the introduction, and parts of chapters 1, 5 & 7, which were included in the publisher's preview or in a newspaper article by the author10. Judging as well as I can from these sources and the table of contents, the book's chapters deal with the following topics:

  1. The first chapter discusses the NYT's reporting on the summer Olympic games held in Berlin in 1936, and the German invasion of Poland in 1939 that started World War 2. I didn't notice any factual inaccuracies in the parts of this chapter that I was able to read, but I'm no expert on these events.
  2. The NYT's reporting on the Ukrainian famine and other journalistic miscarriages from the paper's "man in Moscow", Walter Duranty, whom I've briefly mentioned11.
  3. The reporting by Herbert Matthews for the NYT on the communist revolution in Cuba that put the Castro brothers in power for sixty years12.
  4. Vietnam
  5. The Holocaust
  6. The atomic bombings of Japan
  7. Israel
  8. The Valerie Plame affair
  9. Veterans
  10. The last chapter deals with the paper's recent 1619 pseudo-history project.

The Blurbs: The book is positively blurbed by a motley crew including Glenn Greenwald and Daniel Pipes, which is a good sign.

Date: 2021

Disclaimer: This is a new book and I haven't read it yet, so can't review or recommend it. However, its topic is extremely interesting to me, and I want to read it as soon as possible, despite doubts about its author and foreword writer.


  1. "Preface".
  2. Shakespeare, Macbeth, I, iv, 333-336.
  3. Shakespeare, A Midsummer Night's Dream, III, ii, 1277-1280.
  4. See, especially: Shame, Shame, Shame, 11/30/2020.
  5. See: The Bad News Bearers & Pandemic Pessimism, 3/31/2021 & Tax Day Reading, 5/17/2021.
  6. See: The New York Times Fails at Fact-Checking, Again, 12/23/2020.
  7. See the excerpt from Bari Weiss' resignation letter in: Mail Bag, 8/5/2020.
  8. See: Gabe Stutman, "NYU Professor Uses Tenure to Advance 9/11 Hoax Theory", Observer, 7/26/2017.
  9. Mark Crispin Miller, Fooled Again: How the Right Stole the 2004 Election & Why They'll Steal the Next One Too (Unless We Stop Them) (2005). Apparently, sixteen years ago it wasn't taboo to claim that a presidential election was stolen―I wonder why.
  10. Ashley Rindsberg, "How The New York Times' Misreporting Has Distorted History", The Algemeiner, 5/5/2021.
  11. See: Movie Review: Mr. Jones, 10/15/2020.
  12. See: Anthony DePalma, The Man Who Invented Fidel: Cuba, Castro, and Herbert L. Matthews of The New York Times (2006).

Recommended Reading
May 17th, 2021 (Permalink)

Tax Day Reading

I hope that you've finished your taxes and now have some time to read. Here are this month's recommendations a bit early:


  1. See:
  2. See, for instance: Ivan Couronne, "Catching coronavirus outside is rare but not impossible", Medical Xpress, 10/13/2020. It's also not impossible that you will be hit in the head by a meteorite. Do you wear a helmet when you're outside? If not, why not? See: Justin Nobel, "The True Story of History's Only Known Meteorite Victim", National Geographic, 2/20/2013.
  3. See, for instance: Jacqueline Howard, "'Reassuring' study finds children have small risk of death and severe illness from coronavirus", CNN Health, 8/28/2020.
  4. For the most recent guidelines, see: "Interim Public Health Recommendations for Fully Vaccinated People", Centers for Disease Control and Prevention, updated: 5/13/2021. For the previous guidelines, see: "Interim Public Health Recommendations for Fully Vaccinated People", Centers for Disease Control and Prevention, updated: 4/29/2021. This is the Internet Archive's cache of the page from 5/13/2021.
  5. See: Phillip W. Magness, "The Failure of Imperial College Modeling Is Far Worse than We Knew", American Institute for Economic Research, 4/22/2021.

Disclaimer: I don't necessarily agree with everything in these articles, but I think they're worth reading as a whole. In formatting the excerpts, I sometimes changed the paragraphing.

May 6th, 2021 (Permalink)

Sources for Fact-Checking:
Primary, Secondary & Tertiary

If you've identified a factual claim that you want to check, how should you do it? In the previous entry*, we saw that a factual claim is checked against the facts that either show it to be true or to be false. To do this, you need to find a source or, preferably, sources of the facts. There are three kinds of source that you can use to check factual claims, categorized on the basis of how close they are to the facts:

  1. Primary Sources: These sources are primary because they are the closest to the facts. In some cases, the source closest to the facts is you and your own senses. Suppose that you feel a draft and wonder whether the window is open. Then, the factual claim that you want to check is: "The window is open." To check whether this statement is a fact, you can look at the window and see whether it's open. However, in most research, you won't be in a position to check a claim directly with your own senses. Instead, you must rely upon the reports of others who are or were in such a position, that is, eyewitness reports.

    Example: Suppose that we're dealing with a murder mystery. Then, an obvious primary source would be an eyewitness to the crime. So, if you happened to see the crime take place, your senses would be your primary source of evidence. However, if you were not yourself a witness, other witnesses would be your primary sources. In addition, any photographic or audio recording of the crime would be a primary source. Finally, any other direct evidence found at the scene of the crime, such as fingerprints or the murder weapon, would also be primary sources.

    Primary sources are the strongest type of evidence, but that doesn't mean they're infallible. Even eyewitness reports are notoriously fallible. So, just because you find a primary source does not mean that you're finished fact-checking, even if that source is your own eyesight. Whenever possible, check multiple primary sources against one another.

    Example: Suppose that you're not an eyewitness to the crime, but someone else is. Then, you're going to want to interview the eyewitness, or at least get access to a firsthand report by the witness or a recorded interview. However, don't forget that witnesses are often mistaken. If there is more than one witness then you need access to the others as well. If multiple eyewitnesses disagree with each other, then you'll know that you cannot rely solely on eyewitness evidence; in contrast, if more than one witness agrees, you'll have much stronger evidence than if you must rely on only a single one.

    One problem with some primary sources is that they may be difficult for a layman to understand, so you may need an expert witness to examine and explain it. For instance, specialized knowledge is needed to understand such primary sources as fingerprints or ballistic evidence. This is one reason why you may need the second type of source:

  2. Secondary Sources: A secondary source is one that's not itself a primary source, but based on primary sources. For this reason, secondary sources are often useful in research by pointing you to the primary sources. Another advantage that secondary sources often have over primary ones is that they may be based on more than one primary source. A single primary source may be biased or limited in its perspective, whereas a secondary one may be able to draw on multiple primary accounts.

    Example: In the case of the murder mystery, a news report on the crime would count as a secondary source, assuming that the reporter was not an eyewitness. If the journalist has done a good job, the report will be based on at least one primary source, such as an interview with an eyewitness. If more than one witness or other primary source is consulted, the stronger will be the evidence provided by the report.

    As mentioned above, one type of secondary source is the expert witness needed to interpret some primary sources of evidence. Evaluating expert sources raises special issues of its own that should be addressed in a future entry.

    Unfortunately, many news reports are not based on witnesses or other primary sources; instead, they may be based on nothing more than rumors. Sometimes journalists rely on anonymous sources, making it impossible to evaluate whether the source is firsthand, secondhand, or just rumor. In such cases, news reports should not count as secondary sources, since they're not known to be based on primary sources. For such sources we need a third category:

  3. Tertiary Sources: A tertiary source is one that's not a secondary source, but based on secondary sources. For instance, most reference works, such as encyclopedias, will rely on secondary rather than primary sources. Similarly, textbooks are usually written based on the secondary literature, rather than going back to primary sources. Primary sources come first in strength of evidence, but tertiary sources are in most cases the first ones you should consult.

    Example: If the murder mystery were important enough, it might be used as a case study in a textbook on crime, or have an entry in a reference work. Such an entry should include information on the primary sources of evidence, such as eyewitnesses, as well as secondary sources for the interpretation of technical evidence, such as the report of the medical examiner who examined the victim's body.

The farther a source is from the event or topic in question, the weaker it will tend to be as evidence. So, primary sources provide the strongest evidence, and tertiary ones the weakest. However, finding the primary sources can be difficult. If you can find one, start your fact-checking with a good reference work that gives an overview of the topic and includes pointers to primary or secondary sources. Good research starts with tertiary sources, but only superficial research ends there.

* Earlier entries in this series on fact-checking:

  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

May 2nd, 2021 (Permalink)

2020 Hindsight, Part 3

In part 1, we saw a phony Nostradamus prediction of the coronavirus epidemic1, and in part 2, we looked at some alleged Nostradamus predictions for last year that didn't come true2. This month, let's turn to a genuine quatrain by Nostradamus that has been interpreted in hindsight as predicting the epidemic of 20203. The quatrain in question is II-65, that is, the 65th poem in the second book of Nostradamus' Les Propheties. Here it is, together with the English translation quoted in the article4:

French English
Le parc enclin grande calamité.
Par l'Hesperie & Insubre fera:
Le feu en nef peste et captivité,
Mercure en l'Arc Saturne fenera.
In the feeble lists, great calamity
Through America and Lombardy.
The fire in the ship, plague and captivity;
Mercury in Sagittarius, Saturn warning.

Before considering the interpretation of the poem, let's look at the English translation by Erika Cheetham. Even if you've no knowledge of French, let alone the French of Nostradamus' time, you'll notice that the French version of the word "America"―namely, "Americh" in the Old French spelling used by Nostradamus5―does not appear in the original. Instead, "America" is Cheetham's interpretation of the word "Hesperie", which is the French version of the Latin word "Hesperia". "Hesperia" came from a Greek word meaning "western land", which was used by the Greeks as a name for Italy, which is west of Greece. The Romans used their version of the word to refer to Spain, which was to their west. So, an accurate translation of "Hesperie" would be "western land"6.

Now, America is to the west of France, but translating "Hesperie" as "America" is an interpretation masquerading as a translation. Spain, is also west of most of France as is England. Such tendentious translation is one of the ways in which Nostradamus interpreters mislead English-speaking readers, who will probably not compare the translation to the original.

Another questionable translation is "le parc enclin" as "feeble lists". The author of the article touting this quatrain as a prediction of the coronavirus epidemic thinks that "feeble lists" refers to "the sick and the dead"3. However, "parc" appears to mean much the same as "park" in English, especially one intended for hunting; and "enclin" is similar to English "inclined". Thus, Edgar Leoni translates "le parc enclin" as "the sloping park"7, and Henry Roberts as "the park inclineth"8. I suppose that Cheetham may have been using "lists" in the sense of "inclines to one side", usually used of boats, but where she got "feeble" I don't know. At any rate, I see no connection between an inclined or listing park and the epidemic.

Once you remove the questionable translations, the only things left in this quatrain that suggest the coronavirus epidemic are "peste et captivité", that is, "plague and captivity", with the captivity referring to quarantines and shutdowns. However, plagues are favorite subjects of prophecies, with Nostradamus speaking of "peste" or "pestes" in 26 quatrains, and they are frequent occurrences throughout human history. Moreover, quarantines are nothing new in the history of epidemics, though there are only two quatrains among the Les Propheties that use the word "captivité"9. What reason is there to connect this poem to this epidemic and not another?

Perhaps the astrological information in the last line of the quatrain may allow us to determine when the "peste et captivité" are supposed to take place. The article author claims: "Mercury entered Sagittarius in December 2019, which is when the first cases of coronavirus occurred, and Saturn moved into Aquarius on March 21, right as New York City was going into lockdown.3" Where did Aquarius come from?

The last word of the poem, "fenera", seems to be obscure, making it unclear what it is that Saturn is supposed to be doing. Cheetham translates it as "warning", but her translations are often doubtful, as we've seen. Leoni translates the phrase as "Saturn will fade"7, and Roberts as "Saturn shall wither"8. They seem to be taking "fenera" as a form of the Old French word "fener" which literally meant "to make hay", but in the phrase "se fener" meant "to fade, wither, wax deadish, or decay"10. I don't know how Cheetham got "warning" out of this, nor what Aquarius has to do with it.

The article's author relies on Cheetham's translation of the poem, but makes no mention of what Cheetham herself writes about the last line: "According to Wöllner the next date for this configuration is 7th December 2044, the last being 1839"11. I don't know enough astrology to confirm or deny this, and I'm not sufficiently interested to learn it, so I'll just have to take the mysterious Wöllner's word for it.

In any case, it appears that either the plague predicted in the poem happened in 1839, or it won't happen until another 23 years have gone by. I may not be around on 12/7/2044, but if I am I'll add an update.


  1. 2020 Hindsight, 3/10/2021.
  2. 2020 Hindsight, Part 2, 4/2/2021.
  3. Rae Alexandra, "Perhaps Nostradamus Predicted Coronavirus After All…", KQED, 4/6/2020. Thanks to KQED, a public television station, for wasting our tax money on this junk.
  4. Nostradamus, The Prophecies of Nostradamus, translated, edited & introduced by Erika Cheetham (1981).
  5. Nostradamus uses this word only once in Les Propheties, see: X-66.
  6. Brewer's Dictionary of Phrase & Fable, edited by Ivor H. Evans (Centenary Edition, Revised, 1981).
  7. Edgar Leoni, Nostradamus and His Prophecies (1982).
  8. Nostradamus, The Complete Prophecies of Nostradamus, translated, edited & interpreted by Henry C. Roberts (New Revised Edition, 1982).
  9. I used the following online edition to check the frequency of these words: Nostradamus, The Compleat Works of Nostradamus, accessed: 5/2/2021.
  10. See: Randle Cotgrave, A Dictionarie of the French and English Tongues (1611), under "Fener".
  11. Op. cit. I don't know who Wöllner is, and that name is not in the book's index.

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