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February 23rd, 2009 (Permalink)

Puzzle Number 2

What seven letter word do logicians spell wrongly? No, it's not premiss.


Source: Martin Gardner, Aha! Insight (1978). The puzzle above is similar to one on page 140.

February 22nd, 2009 (Permalink)

Puzzle Number 1

Can you eliminate eight letters from the following sequence of letters to reveal the name of a famous logician?



Source: Martin Gardner, Aha! Insight (1978). The puzzle above is similar to one on page 164.

February 21st, 2009 (Permalink)


I laughed when they said that gay marriage would lead to inter-species marriage.

Two-year old boy marries dog

It brings new meaning to the phrase "a boy and his dog".

February 20th, 2009 (Permalink)


Tom Louvier writes in to ask:

"How would the usual classifications of logical fallacies relate to yours? I understand that you are not using the traditional approach. It would be illuminating to read why."

There's not really one "usual" classification of fallacies, as most logicians who study fallacies seem to come up with their own systems. Unfortunately, I am no exception to this rule of thumb. However, certain categories do tend to occur in such systems and, again, the Taxonomy is no exception.

Previous classification schemes have tended to be "flat", that is, they lack a tree-like structure. They treat all fallacies as having the same level of generality, by grouping them together in only a few broad categories. There are two main ways in which the Taxonomy differs from the more usual classifications:

  1. In the Taxonomy, the fallacies are related by the subfallacy relationship, which is similar to the relationship between genus and species in a biological taxonomy, which gives the fallacy taxonomy its tree-like structure. This means that different fallacies are at different levels of generality, for instance, Ambiguity is a highly general fallacy of which Amphiboly is a more specific form, that is, a subfallacy.
  2. One way of conceptualizing the difference between the Taxonomy and the more usual classification schemes is by means of the concepts of membership and subset in set theory. The subfallacy relation is similar to the subset relation between sets, and has similar logical properties. In the usual schemes, the relation between a fallacy and a classification of it is not the subfallacy relation, but a relation similar to set membership. For instance, the fallacy of Amphiboly is a member of the set of linguistic fallacies, not a subset of it.

In my view, a Taxonomy partially-ordered by the subfallacy relationship is a more fruitful way of categorizing logical fallacies than the traditional flat partitions of the set of fallacies. However, many of the distinctions made by the usual categories are reproduced in the Taxonomy, together with additional structure.

Tom continues:

"Would the subfallacies of ambiguity and vagueness be grouped under the traditional 'fallacies of language'?"

Yes, in the sense that they would be members of the category "fallacies of language". There is no one fallacy in the Taxonomy that corresponds to "fallacy of language", and I'm not sure that such a fallacy would be useful.

Would appeal to ignorance, composition and division, red herring, and special pleading go under the traditional "fallacies of relevance"?

Red Herring is the fallacy in the Taxonomy that represents fallacies of relevance. As a fallacy, "red herring" is usually treated as a particularly egregious irrelevance, or perhaps a catch-all category for irrelevancies that don't fall under any other fallacy. In contrast, Red Herring as I conceive it is the most general fallacy of relevance, and all other fallacies involving irrelevance fall under it. If you look at the Taxonomy under Red Herring, you'll see that none of the other fallacies you mention are subfallacies. That's because what's wrong with these other fallacies seems to be something more than just irrelevance.

In a broad sense, any logical fallacy is guilty of irrelevance, with the exceptions of Begging the Question and the Black-or-White Fallacy. However, this broad a sense of irrelevance is, therefore, useless in making distinctions between different types of fallacy. Specifically, what's wrong with Appeals to Ignorance is not especially that the premisses are logically irrelevant to the conclusion―though they are―it's that the argument puts the burden of proof on the wrong side.

Here's Tom again:

"'Fallacies of induction' could cover your subfallacies of weak analogy and non causa pro causa."

The word "induction" is ambiguous:

  1. I use it for any argument which is not claimed to be conclusive―that is, deductive―but in which the premisses are supposed to make the conclusion probable. In this broad sense, analogical and causal arguments are indeed inductive, so that their corresponding fallacies would be inductive fallacies. However, virtually all the informal fallacies would be inductive fallacies in this broad sense―with the usual exceptions of Begging the Question and the Black-or-White Fallacy.
  2. Some people use the word "inductive" in a narrower sense for a specific type of reasoning, namely, drawing a universal generalization on the basis of specific instances. In this sense, only Biased Sample and Hasty Generalization would count as inductive fallacies.

Back to Tom:

"'Fallacies of presumption' could similarly cover your subfallacies of accident, begging the question, black-or-white, and one-sidedness."

"Fallacies of presumption" has always been a suspect category to me, because it has the appearance of a "miscellaneous" category into which fall those fallacies that don't seem to fit into any other category. It makes some sense that Begging the Question and, perhaps, the Black-or-White Fallacy involve making an unwarranted presumption, but most of the other fallacies in this category seem to get dumped in because they've nowhere else to go.

In the Taxonomy, I'm not so concerned about having a neat partition of fallacies into a small number of categories. Instead, I'm willing to allow some fallacies―such as Loaded Question―to hang out on their own, if they don't seem to fit anywhere. The most important thing is that the Taxonomy show genuine conceptual relationships between fallacies. While the Taxonomy is more complicated than the traditional categories, I hope that study of it will help us understand the fallacies better than such broad categories as "fallacy of language" and "fallacy of presumption" do.

Resource: S. Morris Engel, With Good Reason: An Introduction to Informal Fallacies (Sixth Edition) (2000)

Update (2/26/2009): Tom replies:

The reason I was trying to combine approaches was that I teach my students to analyze fallacies by asking the following questions:
  1. Is my language clear?
  2. Are my premises relevant to the conclusion?
  3. Are my premises (inductively or deductively) sufficient to establish the conclusion?
  4. Are my premises known (by me) to be (factually) true?

These questions relate straightforwardly to the classification used, for example, in How To Think About Weird Things. They do not relate so obviously to your classification. As I understand your response, the answer to question #2 is "no" for all fallacies. #1, #3, and #4 may or may not be broken by an individual fallacy. My mistake would be to use the questions to sort, as well as to analyze, the fallacies. That usage does lead to forcing some fallacies into an inappropriate category.

These are certainly good questions to ask, and there needn't be a conflict between these different ways of classifying fallacies. You're seeking a useful pedagogical approach, whereas I'm trying to classify fallacies according to logical characteristics. Given these different goals, it's likely that the resulting classifications will differ. A pedagogically useful approach should be simple, so the usual partition into a small number of categories is better than a complicated taxonomy. Of course, from a theoretical point of view, such a partition will seem oversimplified.

To show that the two approaches are compatible, here's a classification of all the fallacies currently listed in the Taxonomy in terms of the four questions:

  1. Ambiguity, Vagueness, and all their subfallacies.
  2. Red Herring and its subfallacies.
  3. All of the fallacies under Formal Fallacy would fit here, together with Weak Analogy and its subfallacies and Non Causa Pro Causa and everything under it. One-sidedness might also be classified as an inductive fallacy.
  4. This is an important question, but usually not a logical question. I would include under this question only the Black-or-White Fallacy.

This leaves out a few fallacies which don't seem to fall under any of these questions, in particular, Begging the Question, Appeal to Ignorance, and Loaded Question. You might try to round up these strays with additional questions, or just accept the fact that a few got away.

By the way, I like How To Think About Weird Things very much, but you might want to check out Edward Damer's Attacking Faulty Reasoning, which has a classification scheme similar to your questions.


  1. T. Edward Damer, Attacking Faulty Reasoning: A Practical Guide to Fallacy-Free Arguments (Third Edition) (1994)
  2. Theodore Schick, Jr. & Lewis Vaughn, How to Think about Weird Things: Critical Thinking for a New Age (Fourth Edition) (2004)

February 15th, 2009 (Permalink)

Spotlight on Plagiarism in Wikipedia

One obvious problem with Wikipedia is the potential for plagiarism. Since anyone can add to its articles, there's little to prevent copying from other sources. Given anonymity or concealment behind nicknames, there's no social pressure deterring plagiarism, and small chance that a plagiarizer can be caught or punished in any way.

I've noticed what I suspect is plagiarism of this website in Wikipedia's entries on logical fallacies, but none of it so far has been word-for-word copying. Rather, ideas, examples, references, and sources suspiciously similar to those in Fallacy Files entries are used without attribution. At least in academia, this is considered as much plagiarism as cutting-and-pasting, though it's harder to prove. When dealing with the same subject matter, one can expect a certain amount of similarity, but sometimes these similarities seem to go beyond coincidence. Here's what Wikipedia's own entry says about "plagiarism":

Plagiarism is the use or close imitation of the language and ideas of another author and representation of them as one's own original work. …[P]lagiarism is not the mere copying of text, but the presentation of another's ideas as one's own, regardless of the specific words or constructs used to express that idea.

So, Wikipedia knows what plagiarism is, but I can't find any specific prohibition of it on the site. Of course, one advantage of its free-for-all editing is that anyone who discovers plagiarism can immediately delete it, though there's always the danger that it will be subsequently restored. The possible cases of plagiarism of The Fallacy Files that I've noticed haven't been clear-cut enough to bother trying to eliminate, but I recently came across an egregious case of outright copying.

Four paragraphs of philosopher Michael Labossiere's article on the "spotlight" fallacy are copied word-for-word as a subsection of Wikipedia's entry on biased sample (see the Sources, below). The entire explanation of the fallacy is copied, omitting only the examples at the end and one sentence pointing to related articles, and there is no attribution, citation, or mention of Labossiere's work. According to Wikipedia's history of the biased sample page, it's been this way unchanged for over two years.

Wikipedia gets an "F" on its "spotlight fallacy" paper.



February 13th, 2009 (Permalink)

Blurb Watch: Friday the 13th

Since it's Friday the 13th and the very first "Blurb Watch" that I wrote for this weblog―almost seven years ago!―was for Jason X, the tenth Friday the 13th movie, I'd love to hack and slash at out-of-context blurbs for the latest Friday the 13th movie. Unfortunately, the only ads that I've seen for it have no quotes from critics. I suspect that this is partly because the critical consensus on the movie is negative: it's Metacritic rating is a 34, for "Generally Negative Reviews", and it scores a "Rotten" 28% on the Tomatometer. But I know all the tricks, so I guess that I'll just have to create one myself:

―Roger Ebert, Chicago Sun-Times

Would it surprise you to learn that Ebert gave the movie only two stars out of four? Here's the context:

"Friday the 13th" is about the best "Friday the 13th" movie you could hope for. Its technical credits are excellent. It has a lot of scary and gruesome killings. Not a whole lot of acting is required. If that's what you want to find out, you can stop reading.

Now, maybe I can get a job as a movie ad writer!

Source: Roger Ebert, "Friday the 13th", 2/11/2009

Resource: Blurb Watch, 4/30/2002

February 11th, 2009 (Permalink)

Where's the Harm?

This story is a few years old, but I just came across it:

The elusive number 53, blamed for several deaths and bankruptcies, has finally popped up in the Venice lottery after a two-year wait. Italians had bet more than 3.5bn euros (£2.4bn), hoping that 53 would turn up, in what became a national obsession. Last month a woman drowned herself in the sea off Tuscany after she bet the family savings on 53, Reuters reports. And police said a man living near Florence shot his wife and son and then himself because of his number 53 debts. … A consumer group, Codacons, recently urged the government to ban the number 53 from the draw, to halt the country's "collective psychosis". After 53 finally appeared on Wednesday night, it said it was delighted that Italy's "bewitchment" had been broken.

What fallacy does this news illustrate? (If you don't know, see below.) Those Italians who bet on 53 because it hadn't come up in the lottery for two years believed that it was overdue and, therefore, was more likely to appear than usual. I don't know what randomization method the Venice lottery uses, but if it's a good one then the probability of 53 never changes. In contrast, if there was some reason other than chance why 53 was not a winner for so long, that's evidence that the randomizer is biased against 53. That would be a reason to bet on any number other than 53.

If you were to judge logical fallacies by how much misery they have caused, I suspect that the Gambler's Fallacy would top the list. Just in this one case we have a suicide, some murders, and a lot of people throwing away money in pursuit of an illusion. If you need any evidence of the fact that fallacious thinking is harmful, let this be exhibit A.


Fallacy: Gambler's Fallacy

February 7th, 2009 (Permalink)

Through the Looking Glass, Darkly

Longtime readers of this weblog will remember the comet of Nostradamus that was supposed to strike Earth in the summer of 2004 (see the Resources, below). A new book makes some similar claims, including the prediction that World War III will start this year and continue until 2012.

I haven't read Michael Rathford's The Nostradamus Code: World War III, 2009-2012, but I have studied the sample chapter that's available on the web (see the Source, below). As I've explained previously (see the Resources, below), Nostradamus' prophecies are almost incomprehensibly vague and obscure. Also, most are open-ended, meaning that they can never be falsified by events. So, when someone interprets Nostradamus to have predicted specific events at precise dates, and these predictions predictably fail to occur, it is the interpreter who is refuted, not Nostradamus. So, someone else will come along with a new set of specific predictions that will predictably fail, but not before he's made some money selling his book.

Some of Rathford's predictions are similar to Welch's comet prophecies; for instance, Welch predicted that the comet would land in the Mediterranean Sea and its heat would cook fish. Rathford predicts that a stray nuclear bomb will land in the same sea, also cooking the fish. Both predictions are based on the same poem:

Century II, Quatrain 3
Original Translation
Pour la chaleur solaire sus la mer
De Negrepont les poissons demi cuits:
Les habitants les viendront entamer
Quand Rhod. & Gennes leur faudra le biscuit.
Due to the solar heat on the sea
Of Negrepont the fish half cooked,
The inhabitants will come to cut them
When Rhod. & Gennes will fail them the biscuit.

Obviously, Nostradamus was as bad a poet as he was a prophet. To the extent that this makes any sense at all, it says that the sun is going to half-cook the fish, not a comet or nuclear bomb. Moreover, there's no indication of when this is supposed to happen, so it's an unfalsifiable prediction.

Rathford also predicts the appearance of a comet visible from the Northern Hemisphere soon after the current Pope is assassinated, followed by earthquakes, floods, and other natural disasters that "flatten the nation [the U.S.A.] from end to end". I'm not sure what kind of natural disaster could flatten America, with the possible exception of a new ice age. All this and more will supposedly happen within the next four years.

As an example of Nostradamus hermeneutics, let's take a look at one of the poems upon which Rathford bases his prediction that the Pope will be assassinated:

Century II, Quatrain 97
Original Translation
Romain Pontife garde de t'approcher
De la cite que deux fleuves arrose,
Ton sang viendra auprès de là cracher,
Toi et les tiens quand fleurira le rose.
Roman Pontiff beware approaching
The city that two rivers water,
Your blood will come to be spit nearby,
You and yours when the rose blooms.

Here's how Rathford interprets this verse:

The pope and several of his entourage will be assassinated in late spring when the roses bloom, at a European city that is at the junction of two major rivers.

However, there's nothing to indicate when this is supposed to happen, or what Pope is involved. Welch calls this quatrain one of "Nostradamus' Greatest Hits", that is, a prophecy that has already been fulfilled by the death of Pope Pius VI in 1799 (p. 105)! Not only that, but Welch also gives it a 9.5 rating for "overall impressiveness" (p. 45), which is supposed to measure both its detail and accuracy. Of course, in reality there's nothing in the poem about the Pope being assassinated, or even dying, only spitting blood.

There seems to be some mystery about who Rathford is, for instance, the book's website gives him the title "Dr.", but does not say what his doctorate is in―perhaps he's a podiatrist like Dr. Anna Marie. I left a message on the site asking about his qualifications, but have received no answer.

An earlier version of the book is currently available from Amazon, but gives the title as The Nostradamus Code: World War III, 2007-2012. So, it looks as though the dates of the prophesied events have already been pushed back two years because they obviously haven't yet begun to happen. So, Rathford can just keep selling the same book by advancing the dates a few years with each new edition.

Despite all the assassinations, nuclear warfare, earthquakes, and half-cooked fish, it's revealing that Nostradamus has once again failed to predict the most striking events of recent years. Where was the prediction of the election of the first black American president? What happened to his prophecy of a severe economic recession? Nostradamus is never able to correctly predict anything until after it's happened.

Source: Michael Rathford, "Sample Chapter", The Nostradamus Code: World War III, 2009-2012


Via: Raf Sanchez, "World War III, Papal Assassinations and Poisoned Fish: ‘Dr’ Michael Rathford Revisits Nostradamus", Counterknowledge, 1/3/2009

February 4th, 2009 (Permalink)

Deep Voodoo

About a year ago, in my last entry on the Lancet Iraq civilian death toll studies, I criticized the failure of the researchers to share their data with others. Now, the American Association for Public Opinion Research (AAPOR) has censured the study's lead author, Gilbert Burnham, for violating ethical standards by failing to cooperate with AAPOR's investigation of the studies. I agree with AAPOR's President, Richard A. Kulka:

When researchers draw important conclusions and make public statements and arguments based on survey research data, then subsequently refuse to answer even basic questions about how their research was conducted, this violates the fundamental standards of science….

One thing that separates science from pseudoscience is the openness of science to criticism. As a result, we don't have to take its results on the say-so of any individual scientist. However, if scientists refuse to explain how they got their results, it becomes impossible for others to check those claims. This was one of the problems with cold fusion, as explained by physicist Robert Park:

The information [about cold fusion] given to the press was…devoid of any details that might enable other scientists to judge the strength of the…claim or repeat the experiment. Calls to the University…for more information produced nothing but the press release…. This was no mere breach of etiquette. The integrity of science is anchored in the willingness of scientists to test their ideas and results in direct confrontation with their scientific peers. That standard of scientific conduct was being flagrantly violated….

We now know that the Lancet studies greatly exaggerated the civilian death toll in Iraq, but what we don't yet know is why. It would be a good thing if AAPOR could examine both studies to find out what went wrong, but that won't be possible without cooperation from the researchers. Since Burnham's not a member of AAPOR, this censuring probably won't have any direct effect upon him. However, until he is willing to cooperate with other scientists who want to check his work, no one should take his research seriously.



Update (2/5/2009): Burnham's university, Johns Hopkins, appears to be doing its own investigation of the second Lancet study. Obviously, the school has a much better chance of gaining cooperation in its investigation than AAPOR, since it can do more than publicly censure a nonmember.

Source: Gary Langer, "Nondisclosure Cited in Iraq Casualties Study", ABC News, 2/4/2009

Update (2/24/2009): Johns Hopkins has finished its investigation and suspended Burnham for five years from serving as principal investigator on research using human subjects. This doesn't seem to have anything to do with the inaccuracy of his research, or its politicization. Rather, the full names of some of those interviewed in Iraq were gathered, which violated the original terms of the research accepted by the school's review board. This probably explains Burnham's refusal to fully cooperate with the AAPOR inquiry, given the likelihood that he would get in the trouble that he's now gotten into. Presumably, he refused to hand over copies of the survey forms to AAPOR because, if he did, the presence of the last names would become known.

The review checked the survey forms against the reported data, and for any signs of chicanery in the forms themselves, and found no major problems. However, they did not evaluate the statistical methodology of the study, nor do they seem to have looked into how the survey was conducted in Iraq. So, the report doesn't tell us what was wrong with the study, though it does rule out some possible sources of error. I don't know whether there's any prospect of AAPOR now getting access to the information they needed to complete their inquiry.


February 2nd, 2009 (Permalink)


More snow sweeping across Britain

They should try shoveling.

February 1st, 2009 (Permalink)

New Book

Damian Thompson's new book, Counterknowledge: How We Surrendered to Conspiracy Theories, Quack Medicine, Bogus Science and Fake History, looks promising. It might make a good Book Club selection. According to the book's website (see the Resource below) Thompson is an historian and sociologist of religion.

I like "counterknowledge" as a term covering pseudoscience, pseudohistory, conspiracy theories, and other types of bogus scholarship. I'm not as fond of the subtitle, since I for one haven't surrendered to counterknowledge, and I assume that Thompson hasn't either. However, I suspect that the subtitle was supplied by the publisher, who probably thought that it would help to sell books. If a Fallacy Files book is ever published, it's subtitle will probably be something like "How Illogic Turned Our Brains to Green Jello that Leaked from Our Ears".

It would be nice to get a review copy.

Resource: "Counterknowledge". The companion website for the book, it has an accompanying weblog that is more active and interesting than is usual for a book's promotional website. Unfortunately, there are no free chapters or selections from the book that I can find; just a bunch of blurbs.

Solutions to the Puzzles:


    The name revealed is "ARISTOTLE". The eliminated letters spell out "EIGHT LETTERS".

  2. Wrongly

Explication (2/28/2009): Both puzzles are based on a type of ambiguity that results from ignoring what logicians call "the use/mention distinction". This is the distinction between using a word to refer to what it means, or to refer to the word itself. The difference is easier to illustrate than explain.

Here's a simple example. Suppose that Poochie is the name of a dog. Consider the two sentences:

  1. Poochie has seven fleas.
  2. Poochie has seven letters.

1 uses the name to refer to the dog, whereas 2 mentions the name. Logicians usually use quotation marks around a word to indicate that it is being mentioned rather than used. So, the above two sentences would be written:

  1. Poochie has seven fleas.
  2. "Poochie" has seven letters.

Sometimes mentioned words are put in italics, instead. Either convention avoids use/mention ambiguity, but the use/mention distinction is frequently ignored in popular writing. Both puzzles play upon use/mention ambiguity to fool you, leading you to think that they are using a word or phrase instead of mentioning it. If we use the conventions to distinguish between use and mention then the puzzles are no longer puzzling:

  1. Can you eliminate "eight letters" from the following sequence of letters to reveal the name of a famous logician?


  2. What seven letter word do logicians spell wrongly? No, it's not premiss.

Alternative Solution to Puzzle 1: Chris Cooper came up with a clever alternative solution to the first puzzle. Here's his description:

I first guessed that Aristotle was the logician, since I could see his name buried in there. I saw that twelve letter instances, not eight, had to be removed to get this, and was puzzled. I then decided that perhaps you were playing on a possible ambiguity in the phrase "eight letters" and that the removed letters were of eight different types. The sequence of letters I removed was:


Which contains the eight different letters:


Chris' solution of the puzzle was based on a different type of distinction than the intended solution, namely, the distinction between types and occurrences. This distinction is best illustrated by the question "How many letters are there in the phrase 'eight letters'?" There are two correct answers to this question:

  1. There are eight types of letter.
  2. There are eleven occurrences of letters, including three occurrences of the letter "E".

Thus, the word "letter" is ambiguous between "letter type" and "letter occurrence". When I constructed the puzzle, I had no idea of including an alternative solution based on an alternative type of ambiguity, so it was an act of serendipidy on Chris' part to solve the puzzle this way.

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