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November 24th, 2018 (Permalink)

Another Meeting of the Logicians' Club

The Logicians' Club1 is an organization for perfect logicians who assume nothing and never make a mistake. Moreover, when asked a question, perfect logicians answer with the exact truth and never volunteer information. As you might expect, not many people are eligible for membership. In fact, the current membership of the club consists of three logicians, appropriately known only as A, B, and C.

Once again, the club decided to hold its monthly meeting at a local tavern. In fact, it was the same tavern where the previous meeting was held. When the three logicians had seated themselves at a table, the same waiter who had served them at their previous meeting approached. Naturally, after his previous experience with them, the waiter was nervous, and he carefully avoided wording his question in the same way.

"Would all three of you like a beer?" he asked with trepidation.

"I don't know", said A.

"I don't know", said B.

"Yes", said C.

The waiter left the table and returned a few minutes later carrying a tray with three glasses of beer on it. He set a glass of beer on the table in front of each logician. Each of the three raised a glass and sipped the beer. The waiter sighed with relief.

Why did the three logicians answer the way they did?


Note: For a previous meeting of the club, see here: A Meeting of the Logicians' Club, 9/26/2018.

November 23rd, 2018 (Permalink)

Recommended Reading and Viewing

Are you tired of watching football and parades yet? Here are some recent articles and videos for this long holiday weekend that may be of interest to readers of The Fallacy Files.

November 22nd, 2018 (Permalink)


On this day of thanksgiving, thanks to all of those who have supported The Fallacy Files since last year! The Fallacy Files is an Amazon Associate and, with the holidays upon us, please consider doing any shopping at Amazon by way of one of the links from this site. It won't cost a penny extra and will help keep The Fallacy Files going for another year.

November 21st, 2018 (Permalink)

Tied Up in Nots

Speaking of accentuating the positive and eliminating the negative, as I just was1:

[Some woman I've never heard of] has had to pulp the first copies of her latest book after a quote on the cover mistakenly said she “never fails to disappoint”. [She] said the “nightmare” endorsement was an honest mistake and was meant to say she “never fails to deliver”. The less-than-flattering quote made it past all proofreaders at publishing house Allen & Unwin, and was spotted only when advance copies…had been sent out. “[She] never fails to disappoint, and this book is an easy, interesting read that people in a lot of professions…could learn something from,” the uncorrected quote said. It was printed due to “a proofing error made by our editorial department”, Allen & Unwin said. [She] told Sydney’s Daily Telegraph the mistake made it past six proofreaders at Allen & Unwin, and it was a friend of hers, who had received an early copy, who pointed it out.2

"Never fails to disappoint" has three negations concealed in it:

  1. "Never" means "not ever".
  2. "Fails" means "does not succeed".
  3. The prefix "dis-" is a negative one, and "disappoint" apparently at one time meant "remove from an appointment", that is, to deprive of a position or job. To be "disappointed", in this earlier sense, was no doubt a frustrating and discouraging experience, leading to its current sense.3

The human mind seems to have difficulty understanding more than two negations at a time, which is probably why the mistake was not spotted earlier. Luckily, because two logical negations cancel out, it's usually4 possible to eliminate all but at most one negation. Case in point, since "never fails" means the same as "always succeeds", the original blurb could have been reworded: "always succeeds in disappointing". Restated this way, the mistake would have been immediately obvious.

Here's another example of a triple negation from a couple of years ago:

A U.S. judge said Tuesday that a celebrated artist was right when he insisted he didn't paint a work now owned by a retired prison worker, a finding that likely ensures the piece will now be worth a fraction of the previous estimated value of $10 million or more. … This case created a stir in the art world, where the principle is widely accepted that artists' word on whether a work is theirs or not is final. … Some artists worried the case could set a bad precedent and lead to similar lawsuits, said Amy Adler, who teaches art and the law at New York University School of Law. "This case inspires terror in some artists who fear they could end up in court for denying that a work they did not do isn't theirs," Adler said.5

The quote of Amy Adler at the end has three negations in it: "deny", "not", and "isn't" (is not). Assuming that Adler was quoted correctly, what does the sentence actually say? Does it convey what it appears she meant to say, or did she get tangled up in negations?

The negations in this sentence all occur in the final part describing what some artists fear they could end up being sued for, namely, "denying that a work they did not do isn't theirs". To disentangle these negations, let's proceed in a step-by-step fashion.

First of all, a work they―the fearful artists―didn't do is one that someone else did. Let's call this other artist who actually did the work "X". Then the phrase in question becomes: "denying that a work X did isn't theirs (the fearful artists)".

Secondly, to deny something is to claim that it is not the case, so to deny that "a work X did isn't theirs" means to claim that it is false that X's work isn't theirs. Now, it should be clear that these two negations cancel out, and this is equivalent to claiming that X's work is theirs.

So, if we put this together, the original claim is equivalent to: "This case inspires terror in some artists who fear they could end up in court for claiming that a work they did not do is theirs", which has only one negation. Surely, however, there's always been a danger of being sued or even arrested for claiming that someone else's work is your own. So, this can't have been what Adler meant to say.

Moreover, the case was about an artist who denied that he had painted a particular painting that was alleged to have been his work. So, he did not claim that someone else's painting was his own, but denied having painted it. The artist was sued by the owner of the painting since the denial had led to the painting losing most of its value.

It appears that everyone from Adler on up to the editor of this article was deceived by those three little negations.


  1. See the previous entry.
  2. Naaman Zhou, "‘Never fails to disappoint’: Roxy Jacenko book pulped after cover misprint", The Grauniad, 11/18/2018. Thanks to Lawrence Mayes for calling this article to my attention.
  3. John Ayto, Dictionary of Word Origins (1991). Note that "unappointed" does not mean what "disappointed" used to mean, rather it's an adjective referring to a position that is not an appointed one. I can't think of a single word in current English meaning "to revoke an appointment".
  4. I write "usually" here because some double negations cannot be eliminated without changing meaning. For instance, to say that something is "not unkind" is not the same as calling it "kind", because some actions are neither kind nor unkind. In other words, "unkind" does not mean "not kind", rather it says something logically stronger.
  5. Michael Tarm, "US judge: Renowned artist didn't create disputed painting", Associated Press, 8/23/2016. Via: Ann Althouse, "This case inspires terror in some artists who fear they could end up in court for denying that a work they did not do isn't theirs.", Althouse, 8/26/2016.

November 18th, 2018 (Permalink)

Rules of Argumentation: Introduction

You got to accentuate the positive
Eliminate the negative
Latch on to the affirmative
Don't mess with Mister In-between 1

This entry is an introduction to a series of entries offering a first draft of a set of positive rules for reasoning. Starting next month, I plan to present a new rule each month until the set either seems to be logically complete or I run out of ideas. At this point, I don't know exactly how many rules there will be though I expect, for reasons explained below, that more than a dozen will be necessary.2

Is there a set of positive rules that would cover the same logical territory as the fallacies such that, if you obeyed all of these rules, you would thereby avoid committing any of the fallacies? If you think of a logical fallacy as a "Thou Shalt Not…" commandment, then of course one can have a set of positive rules simply by negating the commandments. For instance, Red Herring is the most general fallacy of irrelevance which, if expressed as a rule would be: Don't be irrelevant! You can turn this negative rule into a positive one: Be relevant! You could do the same thing with all of the other logical fallacies.

Unfortunately, a set of positive rules corresponding one-to-one to the entire taxonomy of fallacies would be too large to be useful3. What seems to be needed is a smaller set of rules that would cover most, if not all, of the fallacies. There are already at least two such sets of rules, so that it isn't necessary to start from scratch:

  1. The Pragma-Dialectical Approach (P-DA): This grandly-named research program was initiated by Frans van Eemeren and Rob Grootendorst4. The centerpiece of the P-DA is a set of "Ten Commandments for Critical Discussants"5, which seems to have been intentionally devised to cover all of the traditional formal and informal logical fallacies.

    The P-DA rules cover the logical territory. The main problem with them is that many are so broad and general that they're not much practical help in improving your reasoning or critiquing that of others. For instance, the fourth commandment is in part: "Standpoints may not be defended by…argumentation that is not relevant to the standpoint."6 In other words, like the hypothetical Red Herring rule mentioned above: Be relevant! But what's relevant? Most arguers who violate the rule think that they are being relevant. So, it's correct but useless as advice.

  2. Damer's Rules: T. Edward Damer, in his textbook Attacking Faulty Reasoning7, provides a set of a dozen rules that he calls "A code of conduct for effective rational discussion"8. There is much overlap between Damer's and the P-DA rules; for instance, Damer's sixth rule, "The Relevance Principle" states: "One who presents an argument for or attacks a position should set forth only reasons or questions that are directly related to the merit of the position at issue."9 In other words, it's our old friend "Be relevant!" again.

To be of practical value to the reasoner, what seems to be needed is a set of rules that would cover all or at least most of the logical territory, but would be more specific than the highly general P-DA or Damer rules. However, it wouldn't be helpful to drill all the way down to the leaf nodes in the Taxonomy, because that's too specific and would produce too many rules. So, somewhere in between the overly-general P-DA/Damer rules and the overly-specific leaves of the Taxonomy would be more helpful to those trying to improve their own reasoning or that of others. That's what I'm going to attempt to do with this series of entries. Stay tuned!


  1. Harold Arlen, "Accentuate the Positive".
  2. Thanks to Kelly Patrick Gerling for asking about a taxonomy of positive rules.
  3. Of course, you can say the same thing about the taxonomy itself, namely, that there are too many fallacies. However, I didn't come up with most of them, I just taxonomized them, so don't blame me!
  4. See: Frans H. Van Eemeren & Rob Grootendorst, A Systematic Theory of Argumentation: The Pragma-dialectical Approach (E&G 1). For a shorter presentation, see the same authors': "The Pragma-Dialectical Approach to Fallacies" (E&G 2), from Fallacies: Classical and Contemporary Readings, edited by Hans V. Hansen & Robert C. Pinto (1995), pp. 130-144.
  5. E&G 1, pp. 190-196.
  6. E&G 1, p. 192.
  7. T. Edward Damer, Attacking Faulty Reasoning: A Practical Guide to Fallacy-Free Arguments (Third Edition, 1995).
  8. Damer, Chapter 8.
  9. Damer, p. 179.

November 16th, 2018 (Permalink)


… As a country, we still have a lot of work to do. We need to agree on some basic rules for civil discourse.

There are many ideas that we will never agree on. The left and the right have different ways of approaching governance, based on contrasting philosophies. But many of the ultimate goals―economic prosperity, better health care and education, etc.―are the same. We just don’t share the same vision of how to achieve them.

How, then, do we live together in this world of differing ideas? For starters, let’s agree that the ideas are fair game. If you think my idea is awful, you should say as much. But there is a difference between attacking an idea and attacking the person behind that idea. … It’s also generally a good indication that the attacker doesn’t have a solid argument and needs a way to end debate before it has even begun.

Similarly, people too often attack not just an idea but also the supposed intent behind an idea. That raises the emotional level of the debate and might seem like it strengthens the attacker’s side, but it’s a terrible way to make a point. Assuming the worst about your opponents’ intentions has the effect of demonizing their ideas, removing the need for sound counter-reasoning and fact-based argument. That’s not a good environment for the exchange of ideas. … *

* Dan Crenshaw, "SNL mocked my appearance. Here’s why I didn’t demand an apology.", The Washington Post, 11/13/2018

Answer to Another Meeting of the Logicians' Club: The waiter asked the three logicians whether all three of them would like a beer. A wanted a beer, but didn't know about B or C. Similarly, B wanted a beer, but didn't know about C. C also wanted a beer and reasoned as follows.

If A had not wanted a beer, then A would have known that it was false that all three of them wanted beer. So, A would have answered "No" to the waiter's question. Thus, the fact that A answered "I don't know" meant that A really wanted a beer. Similar reasoning applies to B. Therefore, when both A and B answered "I don't know", C knew that all three of them wanted a beer. Thus, C was able to answer correctly "Yes".

Note: This puzzle is based on a "three logicians walk into a bar…" joke that appears to be traditional, so I don't know who invented it. Of course, the wording above in terms of the Logicians' Club is my own. This puzzle is fictional; any resemblance of the characters to actual logicians is purely coincidental.

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