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July 7th, 2019 (Permalink)

Rule of Argumentation 61: Defend your position!

This is how arguments usually start: someone makes an affirmative claim that someone else either denies or at least doubts and challenges. If you are the person making a claim and someone challenges it, the burden is on you to defend that claim. If you cannot or do not wish to defend it, then you should withdraw it2.

You may be familiar with the notion of burden of proof in the Anglo-American legal system. In a criminal case, the burden of proof is on the prosecution to prove the defendant's guilt beyond a reasonable doubt. At the very least, the prosecutor must present a prima facie3 case for guilt. If the prosecution succeeds in presenting a prima facie case then the burden of proof switches from the prosecution to the defense. However, if the prosecutor fails to present such a case then the defense wins, that is, the defendant need not even present a case unless the prosecution meets its burden of proof.

Another way of making this same point is that in the Anglo-American legal tradition there is a presumption of innocence, that is, the defendant is presumed innocent until proven guilty. The presumption of innocence is the other side of the burden of proof coin: the burden is on the prosecution and the presumption is in favor of the defendant. If the prosecutor meets the burden with a prima facie case, then the burden and presumption switch: the burden is then on the defense to rebut the prosecution's case sufficiently to show a reasonable doubt of the defendant's guilt.

The notions of burden of proof, presumption, prima facie evidence, and the shifting of the burden of proof can all be extended from the legal realm to argumentation in general. However, it's not obvious who gets the burden and who gets the presumption, that is, who plays the role of the prosecutor and who the defendant?

The answer is that the burden is on the affirmative rather than the negative, that is, on he who affirms as opposed to she who denies. The reason for this is an asymmetry between affirmative claims and denials, namely, that it is much easier to find evidence for an affirmation than a negation4. Moreover, unless they just blurt out claims for no reason, those who introduce a claim should be able to produce some evidence to support it. In contrast, you may be skeptical of a claim without having studied or considered the matter enough to present evidence against it.

The burden of proof is not all or nothing, but comes in degrees. If you assert a plausible claim then the burden of proof will be light, whereas an implausible claim places a heavy burden on you. This is the basis for the familiar saying that extraordinary claims require extraordinary evidence5.

Logical fallacies that result from attempts to evade the burden of proof include6:

So, the burden of this rule is that if you make an affirmative claim, be prepared to defend it. If, in contrast, you are the challenger and the proponent of the challenged claim makes a prima facie case, then accept the burden of proof. It is now up to you to either make a case against the claim, or to accept it.

Next Month: Rule 7


  1. Previous entries in this series:
    1. Rule of Argumentation 1: Appeal to reason!, 12/14/2018.
    2. Rule of Argumentation 2: Be ready to be wrong!, 1/26/2019.
    3. Rule of Argumentation 3: Focus on claims and arguments!, 2/13/2019.
    4. Rule of Argumentation 4: Be as definite as possible!, 3/8/2019.
    5. Rule of Argumentation 5: Be as precise as necessary!, 5/29/2019.
  2. As with all the rules discussed in this series, this is a rule of thumb, that is, a rule that has exceptions. For this rule, common sense is an exception. For instance, a person who asserts that every living thing eventually dies does not bear the burden. Instead, those who challenge such a claim must make a prima facie case against it, and only then does the burden shift to the claimant.
  3. Latin for "at first sight". See: Eugene Ehrlich, Amo, Amas, Amat and More: How to Use Latin to Your Own Advantage and to the Astonishment of Others (1985). A prima facie case for a claim is one that is sufficiently strong to prove the claim unless successfully rebutted.
  4. It is often said that you can't prove a negative, which is over-stated but a good rule of thumb. For an explanation of how much truth there is in this saying, see: Logical Literacy: "You can't prove a negative.", 3/14/2015.
  5. Popularized by the astronomer Carl Sagan, see: Broca's Brain: Reflections on the Romance of Science (1980), p. 73.
  6. For more on each fallacy, see the entries under the names of the fallacies available from the drop-down menu in the navigation pane to your left.

July 4th, 2019 (Permalink)

An Independence Day Puzzle at the Logicians' Club

In July of 2019, the Logicians' Club* held its monthly meeting on the fourth. To celebrate the holiday, the members played a game. On this day, its three regular members were in attendance: Mrs. A, Miss B, and Mr. C. It was the latter who suggested the game and organized it for the other two members to play. They met in a private room of the tavern where the club meetings were held.

"Fellow logicians," Mr. C began impressively after clearing his throat, "I have here a bag of patriotic hats," he said, holding up a large opaque bag. "Two of the hats are red, two are blue, but only one is white." He reached into the bag, pulled out a white hat and placed it on his own head.

"In a few minutes," he continued, "I will turn out the lights and pull two hats out of the bag. Then I will place a hat on each of your heads. When I turn the light back on, both of you will be able to see the color of the other's hat, but you won't be able to see your own. I will ask each of you to guess the color of your own hat by whispering in my ear so that the other player won't know your guess. If at least one of you is right, you will both win a prize which you can share.

"Now, I'm going to step out of the room for a few minutes and allow you time to confer. It won't be cheating if you agree between you on a strategy for playing the game. Remember two things: first, only one of you has to guess the color of her hat correctly in order to win the prize―it doesn't matter whether the other player's guess is incorrect; second, if you win you will share the prize, so this is not a competitive game. Good luck!" And he left the room.

Is there a strategy that the two logicians can use to ensure that they win the prize? If so, what is that strategy?

* For other meetings of the club, see:

(Added 7/9/2019) An anonymous reader wrote in wondering whether Mr. C could have taken the white hat that he put on his own head and put it on one of the two players when the lights were out. Of course, he could have, but rest assured that he didn't.

(Added 7/5/2019) Thanks to Lawrence Mayes for pointing out a loophole in the description of the game which has now been closed by amending this sentence.

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June 27th, 2019 (Permalink)

The Big Democratic "Debate", Part 1

The first of two "debates" of candidates for the Democratic party's nomination for president was held last night, and the second part will be tonight. I have some general comments about these so-called debates:

That's the whole forum in a nutshell. I don't mean to criticize the candidates quoted above specifically since none were significantly different. These candidate forums may serve some useful purpose for anyone planning to vote in a Democratic primary, but as a "debate" about substantive political issues they're a waste of two hours.

Given the above, I doubt that I will have anything additional to say about the second forum tonight, since it will probably be more of the same.


  1. Jeremia Kimelman, "Full transcript: 2019 Democratic debate Night One, sortable by topic", NBC News, 6/27/2019
  2. Allan Smith, "NBC announces five moderators for first Democratic debate", NBC News, 6/11/2019

June 22nd, 2019 (Permalink)

Last Visit to the Hilbert Hotel

In our previous visits to the Hilbert Hotel, we saw that even though the infinite hotel was full it could still provide rooms for new customers1. We also learned that The Hilbert Company, Inc., that owns the hotel also owns an infinitely long railroad line and an infinitely long train that runs on it2. What we didn't learn at the time is that the company owns an infinite number of infinitely long trains running on an infinitude of infinitely long tracks.

So, one day an infinite number of such trains pulled up at the hotel each carrying an infinite number of passengers, all desiring a room for the night. As usual, the "No Vacancy" light was lit. The clerk on duty that day was the same one we met previously who knew how to provide new rooms for any finite number of new guests even when the hotel was full. He also had learned from the manager how to accommodate an infinite number of new arrivals from one of the infinitely long trains.

However, how was he to find rooms for an infinite number of guests from an infinite number of trains? Even if he opened up an infinite number of rooms by moving all of the current guests into the even numbered ones, as he had been taught by the manager, the very first train would fill up all the odd numbered rooms. Of course, once the hotel was full again, he could do the same trick a second time, but how could he do it an infinite number of times?

Instead of trying to accommodate the new customers train by train, the clerk thought that maybe he should start with the first passengers in each train. However, he soon realized that this would not work, either: since there were an infinite number of trains, there were an infinite number of first passengers. He would end up filling up the whole hotel with just the first passengers in each train, and then he'd have to repeat the same procedure an infinite number of times.

The clerk didn't want to bother the manager again, so he thought hard for a few minutes. He could once again move all of the current guests into the even-numbered rooms, thus opening up the odd-numbered ones, of which there were an infinite number. But how could he make sure that every one of the new guests received a distinct room? Can you help the clerk solve the puzzle?



  1. See: No Vacancy at the Hilbert Hotel, 4/29/2019
  2. See: Still No Vacancy at the Hilbert Hotel, 5/13/2019

June 12th, 2019 (Permalink)

Wolff's Howlers (Updated: 7/16/2019)

Michael Wolff, author of Siege: Trump Under Fire, is himself under fire for factual errors in the new book. Many of the errors singled out for criticism seem minor, but one is a whopper:

In the book, Wolff claimed to possess copies of special counsel Robert Mueller's alleged March 2018 draft indictment of Trump on counts of obstruction of justice. However, Mueller's office has asserted that the documents "do not exist."1

Of course, the fact that Mueller's office denies the existence of the draft isn't dispositive, but given the denial the burden of proof is now on Wolff to substantiate his claim. However, Wolff has so far not produced the alleged draft:

Pressed on his sourcing, and whether he would release copies of the supposed Mueller draft indictment memos he claims to have gotten, Wolff averred2. He couldn’t release copies, he said, because that might expose one of his anonymous “authoritative” sources. “You just have to trust me,” he said.3

Trust is earned, but so is distrust, and I think Wolff has earned the latter. In addition to the non-existent indictment, all or most of Wolff's sources for the book are anonymous except for one: Steve Bannon, who does not inspire confidence, to put it mildly.

Just as we saw with Naomi Wolf's new book last month4, this is not the first time Michael Wolff's reporting has come under siege for factual errors. His previous book, Fire and Fury, was a bestseller but apparently factually-challenged5.

I'm less interested in the specifics of Wolff's errors than in what this, taken together with the recent Naomi Wolf blunder, says about the state of the fact-checking of books. According to a Washington Post report about Wolff's previous book:

How did mistakes like these get past a fact-checker? Neither Wolff nor his publisher, Henry Holt, responded to…inquiries about how―or whether―“Fire and Fury” was vetted. Whether is a real question here. In many cases, publishers of nonfiction books such as Wolff's perform little, if any, fact-checking, leaving authors with a choice: pay out of their advances for someone to review their work or skip this pesky step altogether. Wolff thanked three people for fact-checking, in the book's acknowledgments section, but did not describe the scope of their work. “In my experience, publishing houses rarely, if ever, pay for fact-checking,” said Robert Liguori, a freelance fact-checker…. “I can't speak to whether any publishers have their own checking departments, but I have never heard of a major publishing house that has an internal staff to check its books.” Liguori said he has always been hired by careful authors, never by a publisher. Dan Kaufman, who has fact-checked books…told me the same thing.5

So, what happened to all those "editors, copyeditors and proofreaders for each book project"4? It was Naomi Wolf's publisher that boasted of them, but doesn't Henry Holt have any? Not all fact-checking is done by people called "fact-checkers", as Sarah Harrison Smith has written:

Fact checkers are everywhere, though many don't call themselves by that name. Editors, copy editors, writers, and researchers for print, radio, and even television verify facts as part of their jobs. Media that don't employ nominal fact checkers often divide the work of a fact checker among employees who do lots of other things, too.6

For this reason, I don't agree with the following:

Author…Susan Orlean told me that she was “flabbergasted” when she turned in a manuscript for her first book and learned that her publisher did not plan to check her work. But she said she has come to understand that “publishers simply can't do it.” “I mean, to properly fact-check a book basically means re-reporting a book,” she said. “That's how you do it. And a publisher can't do that, so I don't think it's malfeasance on their part or neglect. I think it's just not practical for them to do it, and they're assuming that you've done it.”5

Fact-checking is not the same as reporting, or at least it shouldn't be. Fact-checkers wouldn't be expected to redo all of the reporting that goes into a book such as Wolff's, but to check those things that can be quickly and easily checked. For instance, how hard would it have been to pick up a phone and call Mueller's office about the alleged draft indictment? Presumably, some reporter did just that, which is why the office issued the denial.

All of which raises the question: why didn't Wolff himself make such a call? I suspect that the reason is the obvious one that he didn't want to know. It wouldn't have been impossible or even impractical to check this; it just would have been too risky. The book is currently number four on The New York Times hardcover non-fiction bestseller list7.

Update (7/11/2019): Since I wrote this a month ago, the Jeffrey Epstein case has become a major scandal. According to journalist Vicky Ward:

A few years ago the journalist Michael Wolff wrote a profile of him for New York magazine that was meant to “rehabilitate” Epstein’s image and would tell of all the billionaires who still, secretly, hung out with Epstein. The piece had “fact-checking” issues and never ran. Even so, the notion that it was considered is mind-boggling.8

So, fact-checking issues, again, though I wonder whether the fact that "fact-checking" is in quotes suggests that that was just an excuse for killing the article, with the real reason being something else. Perhaps the following excerpts from an article that did run in New York magazine during the time that Epstein was first being prosecuted can help explain why the "mind-boggling" profile was even considered:

Vanity Fair columnist Michael Wolff met him in the Internet bubble, in the late nineties, when Epstein invited him and a group of scientists and media types to fly to a conference on the West Coast in his beautiful 727. “…[A]fter fifteen to twenty minutes, [Wolff said] Jeffrey arrives. … And he was followed onto the plane by―how shall I say this?―by three teenage girls not his daughters. Not adolescent girls. These are young, 18, 19, 20, who knows?…”9

17, 16, 15, 14, who knows? Continuing:

Soon after, Wolff was invited to tea at the house on East 71st Street. He understood that there was a purpose to the cultivation. Epstein was shifting his view to media…. In 2003, he became a discreet confidant to Wolff during the period when Wolff was involved in a bid for New York Magazine. … “He has never been secretive about the girls,” Wolff says. “At one point, when his troubles began, he was talking to me and said, ‘What can I say, I like young girls.’ I said, ‘Maybe you should say, ‘I like young women.’”9

Let me see if I have this straight: a few years after this Wolff was trying to write a profile for the same magazine to rehabilitate Epstein? Mind-boggling, indeed.

Update (7/14/2019): Yesterday, The New York Times published a lengthy article detailing some of Epstein's attempts to rehabilitate his image after his conviction, and the extent to which those attempts were successful. Wolff is not mentioned in the article, but the following passage is suggestive:

Some of the respect Mr. Epstein…drew on was manufactured…. A writer employed by his foundation churned out the news releases, and Drew Hendricks, the supposed author of a Forbes story calling Mr. Epstein “one of the largest backers of cutting edge science,” conceded in an interview that he was given $600 to post the pre-written article under his own name. (Forbes removed the piece after The New York Times published its article.)10

This passage raises some questions: Was Wolff paid by Epstein to write the article that was supposed to help rehabilitate his reputation? Or was he, like Hendricks, paid simply to put his name on an article written by someone else11? Did New York magazine find out about this and kill the article, using "fact-checking" as an excuse? These are just questions that I don't know the answer to, but if the answer were "yes" to any of them, that would help explain the otherwise "mind-boggling" article.

Update (7/16/2019): The fact-checker for Wolff's "mind-boggling" profile of Epstein appears to have been Alex Yablon, who titteringly cheeped:

In a new piece @VickyPJWard reports that New York Magazine was going to run a profile on Epstein by Michael Wolff that was killed out of fact checking concerns. Fun fact: I was the checker who killed it! One of my weirdest fact-checking experiences. Wolff let Epstein dictate the piece. He made some agreement that all fact questions would go through Epstein and only Epstein. In the piece, Wolff reported various powerful men still hung out with Epstein―but gave me no proof. I was not allowed to call them for comment. Not surprisingly, NY Mag's lawyers weren't thrilled about a story that alleged various rich and potentially litigious men socialized with a sexual predator without any proof or calling them for comment. As I recall the editor wasn't even aware Wolff had made this agreement. This is really more of a Michael Wolff story than a Jeffrey Epstein story.12

Yes, which is why I'm interested in it. This seems to answer at least part of one of my questions, namely, did someone other than Wolff write the profile? According to Yablon, Epstein himself dictated it! Of course, this answer raises the follow-up question: did Epstein pay Wolff for "writing" it?

It also appears to be the case, if what Yablon says is true, that the profile was killed for genuine fact-checking reasons, since real fact-checking seems to have been ruled out. However, the article seems to have been the result of a corrupt process, since no reporter should allow the subject of a profile to "dictate" it, nor enter into any agreement along the lines of the one described by Yablon. Surely, fact-checking aside, either of these should have been sufficient reason to kill it.


  1. Christina Zhao, "Michael Wolff Defends New Book From Allegations of Factual Inaccuracies in Heated Interview: 'This Critique is Bulls**t!'", Newsweek, 6/8/2019.
  2. "Averred?" Averred what? The author appears not to know the meaning of this word. "Aver" means "affirm" or "declare", and it's a transitive verb but it lacks an object here. What should the author have written? "Demurred", perhaps, which is intransitive and means "objected", and at least sounds similar to "averred". Otherwise, "declined" or "refused" would seem to be what was meant. See:
    • "Aver", Merriam-Webster, accessed: 6/11/2019.
    • "Demur", Merriam-Webster, 5/17/2019.
  3. Michael Isikoff, "Confronted with multiple errors in his new Trump book, a testy Michael Wolff says, 'You have to trust me'", Yahoo! News, 6/8/2019.
  4. See: Wolf's Howler, 5/31/2019.
  5. Callum Borchers, "How did Michael Wolff’s ‘Fire and Fury’ get past a fact-checker? It’s not clear that the book was vetted.", The Washington Post, 1/9/2018.
  6. Sarah Harrison Smith, The Fact Checker's Bible: A Guide to Getting it Right (2004), p. 11.
  7. "Hardcover Nonfiction", The New York Times, accessed: 6/12/2019.
  8. Vicky Ward, "Jeffrey Epstein’s Sick Story Played Out for Years in Plain Sight", The Daily Beast, 7/9/2019.
  9. Philip Weiss, "The Fantasist", New York Magazine, 12/7/2007. Warning: Parental guidance suggested. Not for the squeamish.
  10. Jodi Kantor, Mike McIntire & Vanessa Friedman, "Jeffrey Epstein Was a Sex Offender. The Powerful Welcomed Him Anyway.", The New York Times, 7/13/2019.
  11. For what it's worth, here is that article: Drew Hendricks, "Science Funder Jeffrey Epstein Launches Radical Emotional Software For The Gaming Industry", Forbes, 10/2/2013. This is Bing's cache of the page which is no longer available from Forbes; accessed: 7/14/2019.
  12. "Alex Yablon", Twitter, 7/9/2019.

June 1st, 2019 (Permalink)

Medice, Cura Te Ipsum1

Only the night before, Moran was an unknown 23-year-old student in St. Paul, Minnesota. … Living alone in a new city, she worked at a Chipotle to make ends meet…. That morning, though, she discovered she had become someone else. Strangers were calling her nasty names on social media. Her photo was plastered across internet news sites. A video was circulating online, and she was its villain. In it, she could be seen refusing to serve a group of black men at the restaurant the previous evening.2

The above quote is from an article that tells the story of a woman falsely accused of racism, and the online lynch mob that immediately formed and got her fired. It's a compelling story, and I recommend that you read the whole thing as a cautionary tale. I further recommend that you read it before returning to this entry as I have some criticisms to make of one thing in the article. I will assume that you have done so.

As you've read, the incident reported in the article was another rush to judgment based on a misleading online video, similar to the Covington incident earlier this year3, with similar threats of violence against the victim and her family. As far as I know, no one has yet been actually lynched by one of these mobs, but it's just a matter of time before someone acts on the threats.

As harrowing as the young woman's story is, in the following passage the article itself does something close to the very thing it is describing. It does so by propagating a false accusation of racism in the following claim: "Critics accuse President Trump of normalizing racism by referring to Mexican immigrants as 'rapists'…". As I pointed out last year4, it's a false accusation based on a contextomy.

Almost as bad as spreading this slander is attributing it to some unnamed "critics". This is a weaselly journalistic technique to introduce by innuendo a charge that the journalist doesn't want to have to defend. I'm sure somebody somewhere has accused Trump at some time or other of this, but it's really the journalist who is saying it and at the same time ducking responsibility. If CNN wants to accuse Trump of calling all Mexicans rapists, it should do so openly and stand by it; if it can't stand by it, because it's false, it shouldn't insinuate it.

It's easy to discover that the Mexican rapists accusation against Trump is bunk as not only Politifact but even Salon debunked it last year4. When CNN complains about Trump calling it "fake news"5, I'd be more sympathetic if it would stop publishing things like this.


  1. "Physician, heal thyself", Latin. See: Eugene Ehrlich, Amo, Amas, Amat and More: How to Use Latin to Your Own Advantage and to the Astonishment of Others (1985). This proverb is cited by Jesus in Luke 4:23.
  2. John Blake, "How an internet mob falsely painted a Chipotle employee as racist", CNN, 5/27/2019.
  3. See: Recommended Reading, 1/30/2019, the last two selections.
  4. Meet the Press, 9/25/2018.
  5. Donovan Slack, "Trump to CNN: 'You are fake news'", USA Today, 1/11/2017.

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