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December 28th, 2009 (Permalink)

Spot the Fallacy

Zorza…informs readers that "between 20 and 35 percent of women seeking medical care in emergency rooms in America are there because of domestic violence." Studies by the federal Centers for Disease Control and Prevention and the Bureau of Justice Statistics, an agency of the U.S. Department of Justice, indicate that the figure is closer to 1 percent.

Source: Christina Hoff Sommers, "Persistent Myths in Feminist Scholarship", The Chronicle of Higher Education, 6/29/2009

Sommers…challenged a statement by Zorza in my textbook regarding the high incidence of battered women in emergency rooms. …[T]he Centers for Disease Control Web site…stated, when I checked it on July 15, 2009: …intimate-partner violence, "is a major cause of violence-related injuries. Intimate partners were identified as the perpetrators in 36 percent of all emergency department visits by women who suffered from one or more violent injuries." Similarly, the Bureau of Justice Statistics at the U.S. Department of Justice has reported that 37 percent of all women who sought care in hospital emergency rooms for violence-related injuries were injured by a current or former spouse, boyfriend, or girlfriend…. We also find similarly high figures published in medical journals…. D.C. Berios and D. Grady…found that among 218 women presenting in a metropolitan emergency department with injuries due to violence, 28 percent required hospital admission and 13 percent required major medical treatment.

Source: Nancy K. D. Lemon, "Myths or Facts in Feminist Scholarship?", The Chronicle of Higher Education, 8/10/2009

Can you spot the fallacy in the above exchange between Sommers and Lemon? It's not important whether you can put a name to the error, but can you find it and understand why it's a mistake? When you think that you've got it, click on the link below.

The Fallacy

December 22nd, 2009 (Permalink)

Conspiracies to the Left, Conspiracies to the Right

What are the fallacies behind conspiracy theories? Here are some examples taken from a recent article by David Aaronovitch, author of Voodoo Histories:

By the way, I still haven't received a review copy of Aaronovitch's book, which I'm eager to read.

Source: David Aaronovitch, "A Conspiracy-Theory Theory", The Wall Street Journal, 12/19/2009

Resource: New Book: Voodoo Histories, 5/8/2009

December 15th, 2009 (Permalink)


Philosopher Stephen Toulmin, best known for his book The Uses of Argument, has died. Uses seems to have been influential in rhetoric, and may have spurred interest in the use of diagrams for analyzing argumentation.

Source: Michael Ruse, "Stephen Toulmin, Philosopher, 1922-2009", The Chronicle of Higher Education, 12/12/2009

René Magritte's 'Le Faux Miroir'
December 13th, 2009 (Permalink)


I've previously discussed the fact that the information provided by so-called psychic detectives is usually so vague and general that it's useless for finding missing people, since it will apply to almost any case. Unfortunately, in those past cases (see the Resources below), the missing persons have never been found, so it's impossible to check the information against the facts. Here's a case that's different:

Jeff Howard was a 40-year-old husband and father in December 2006 when he left his home in Thousand Oaks, leaving no trace. Exhaustive searches by police and family haven't generated a clue about what happened to him.

Earlier this year, Howard's body was found in his car in a canyon south of Thousand Oaks. There were two "psychics" consulted:

  1. "Increasingly desperate to find out what happened, his parents turned to a New Jersey-based psychic, Nancy Orlen Weber. She told them…Jeff Howard was living in or near Escondido and suffering from…a type of amnesia."

    This is fairly specific information, though Escondido is a big city, and Weber hedged her information by allowing that he might only be "near" there. Of course, it's all wrong: Howard must have been dead by the time Weber was consulted, and so he didn't have amnesia, nor was he in or anywhere near Escondido.

  2. "Thayla Howard had long been fascinated by the TV show, 'Psychic Detectives,' which features oracles who help law enforcement solve cases. In January 2007, she consulted Virginia-based Noreen Renier, who had appeared on the show many times. Renier told her she thought Jeff Howard was alive and was somewhere northeast of Thousand Oaks. She said she saw him near a 'red and white gas station' and a burned-out, then rebuilt, building on a road less traveled."

    The information about the gas station is very imprecise as many stations have red and white colors in or around them. Since you can't tell by looking at it whether a building that has been rebuilt had once been burned, that information was quite useless even if it turned out to be true. I'm not familiar with the area in which Howard was found but, since it's part of a National Recreation Area, I doubt that there were any gas stations or burned but rebuilt buildings nearby. Renier was also wrong in claiming that Howard was alive, and he was found south of T.O., not northeast of it. The one thing she might have been right about was the road, but given the fact that he and his car had been missing for about a month when Renier was consulted, it's a pretty good guess that he may have taken "the road less traveled". No doubt if he had taken a more heavily trafficked route he would have been found much sooner.

    "After driving thousands of miles following Renier's clues, for which the family said they paid $1,000, the Howards found nothing."

    Has Renier at least refunded their money?



December 10th, 2009 (Permalink)

Check 'Em Out

December 9th, 2009 (Permalink)

Poll Watch

Here's the headline and first sentence of a recent news story:

Obama's 47 Percent Approval Lowest of Any President at This Point

President Obama's job approval rating has fallen to 47 percent in the latest Gallup poll, the lowest ever recorded for any president at this point in his term.

That certainly sounds bad, and it is, but not quite as bad as all that. Obama's approval rating is on the low end, but he has company. Here's the end of the article:

The…11 presidents [since Gallup began polling], … all had higher job approval ratings than Obama at this stage of their tenure. Their ratings were:
  • George W. Bush, 86 percent
  • Bill Clinton, 52 percent
  • George H.W. Bush, 71 percent
  • Ronald Reagan, 49 percent
  • Jimmy Carter, 57 percent
  • Gerald Ford, 52 percent
  • Richard Nixon, 59 percent
  • Lyndon Johnson, 74 percent
  • John Kennedy, 77 percent
  • Dwight Eisenhower, 69 percent
  • Harry Truman, 49 percent
The poll is an average of a three-day tracking of 1,529 adults taken Dec. 4-6. It has a margin of error of 3 percentage points.

So, both Truman and Reagan had approval ratings of only 49% at this same time in their presidencies, which is only two percentage points higher than Obama's record low and within its margin of error (MoE). In reality, Obama is tied with Truman and Reagan for lowest approval ratings at this point in a presidency.

The next day's Gallup tracking poll had Obama's approval rating back up to 50%. Does this mean that three percent of the public went from disapproving of Obama's performance to approving of it overnight? It's possible, but not likely. Rather, what it shows is that changes within the MoE are not significant.


Resource: How to Read a Poll: Margin of Error Errors, Fallacy Watch

December 7th, 2009 (Permalink)


Q: I am trying to use your site to classify this fallacy:

If the voters pass this measure, place P will become a city. Cities have problems with crime. Therefore, if this measure passes, P will have problems with crime.

My first thought was that this is a "reification fallacy", assigning too much weight to whether the word "city" is applied to P. Another one that seems to fit is an over-generalization, the assumption that every city has problems with crime, but the specific fallacy here is that legally applying the word "city" to an area will cause an increase in crime.

I have been looking over your taxonomy, trying to find a place to put this, and I'm still not sure where it fits. Where would you put this fallacy in your taxonomy?―Steve R. Hastings

A: This is a tricky example. The argument that you cite is, in fact, valid, at least if we interpret the second premiss to mean that all cities have problems with crime. If, as you suggest, "all" would be an over-generalization, and we interpret the second premiss as meaning that most cities have crime problems or that cities typically have such problems, then the argument would be invalid. However, it would still be an inductively strong argument.

I don't see what reification has to do with it, though the supposed fallacy of reification is an obscure one―that's why there's no Fallacy Files entry for it.

Also, the argument as you state it makes no reference to causation. I suppose that you might think that causation is what makes the first premiss true: the voters passing a certain measure will cause P to become a city. Moreover, if all cities have crime problems, then the passage of the measure will cause P to have such problems.

Of course, there's obviously something wrong with the notion that merely designating a place a "city" would cause it to have problems with crime. This is "word magic", that is, the superstitious idea that words have magical powers over the objects that they name. However, it's also odd to think that legislation would cause a place to turn into a city. In what sense would it be possible to create a "city" by passing a law?

At this point, I think we get a glimpse of what's wrong with the original argument. Presumably, the voters could designate anything they please a city, even a desert. This is why such a designation has no causal power to bring about a crime wave. When we say that all cities have crime, we mean by "cities" places with large and dense human populations. Given that people are responsible for crime, any place with a large number of people will probably have a large amount of crime. In contrast, no matter what it's called, a desert will have very little crime, since it has so few people.

In other words, the original argument equivocates on the word "city". The first premiss uses "city" as a legal designation: let's call this a "legal city". The second premiss, however, uses "city" to refer to large, densely-populated human settlements, which is the usual sense of the word: let's call this an "actual city". So, we can disambiguate the original argument as follows:

If the voters pass this measure, place P will become a legal city. All actual cities have problems with crime. Therefore, if this measure passes, P will have problems with crime.

This argument is not valid, because there's no logical connection between a legal city and an actual one, given that the voters might make a desert a legal city. However, if the voters designate an actual city as, legally, a "city", that will not cause a crime wave. Whatever crime problem the city has is due to the fact that it has a large, dense human population, and it will continue to have that problem whether or not it is legally designated a "city".

Fallacy: Equivocation

Everybody's Fine
December 4th, 2009 (Permalink)

Blurb Watch:
Everybody's Fine & The Road

The Road

I've previously pointed out that ads for movies sometimes display four stars from a reviewer who uses a system allowing for more than four. A similar trick with stars can be done when the reviewer gives half-star ratings, specifically, if a movie receives three-and-a-half stars. We can see this trick at work in ads for two new movies: Everybody's Fine and The Road. A quick glance at the ads makes it appear that each movie received two four-star ratings―the former from critics Mara Reinstein and Marshall Fine, and the latter from reviewers Roger Ebert and Claudia Puig―but a closer look reveals that the last star has a small "½" inside it to indicate that it's really only half a star. Depending on how large the ad is displayed, it may be difficult to see the fraction at all. The danger of misleading you into thinking that the ratings are four stars could be avoided by doing what many newspapers and magazines do, namely, using a half star instead of a complete star with a "½" in it. Of course, that's assuming that the studios don't want to mislead you.

December 2nd, 2009 (Permalink)


States act to curb 'double dipping'

It's like putting your whole mouth right in the dip!

December 1st, 2009 (Permalink)

The Second Puzzle of the Terrorist Acquaintance

After your first experience helping the Agency for Counter-Terrorism (ACT) with a logical problem, ACT comes to you with another, related but more difficult, problem. As in the first problem, Subject 1 is a known terrorist. Subject Z, however, is known not to be a terrorist. ACT has determined that Subject 1 is connected to Subject Z by a chain of acquaintances, that is, Subject 1 is acquainted with Subject A, who's acquainted with Subject B, etc., who's acquainted with Subject Z. However, ACT does not know whether any of the acquaintances in the chain between 1 and Z are terrorists or not. Moreover, ACT does not know how many links there are in the chain of acquaintances between Subject 1 and Subject Z. Despite that, ACT asks the same questions as before: Is any terrorist acquainted with a non-terrorist, or is it impossible to determine from the information given?


Resource: The Puzzle of the Terrorist Acquaintance, 11/15/2009

Spot the Fallacy: This is a remarkable example of Aristotle's fallacy of "ignorance of refutation", or "ignoratio elenchi" in Latin. Sommers criticized the following claim made by Zorza in Lemon's textbook: "between 20 and 35 percent of women seeking medical care in emergency rooms in America are there because of domestic violence." In defense of Zorza's claim, Lemon cites three pieces of evidence (this is not the only evidence Lemon gives, but the other evidence raises distinct issues):

  1. Intimate partners were identified as the perpetrators in 36 percent of all emergency department visits by women who suffered from one or more violent injuries.
  2. 37 percent of all women who sought care in hospital emergency rooms for violence-related injuries were injured by a current or former spouse, boyfriend, or girlfriend.
  3. Among 218 women presenting in a metropolitan emergency department with injuries due to violence, 28 percent required hospital admission and 13 percent required major medical treatment.

The percentages cited are within, or close to, the range of percentages cited by Zorza, but each of the three claims concerns only those women who go to the emergency room for injuries from violence, whereas the Zorza claim was about all emergency room visits by women. As a result, Lemon's defense of Zorza's claim fails because it misses the target, that is, she actually ends up defending a different claim: "between 20 and 35 percent of women seeking medical care in emergency rooms for injuries from violence are there because of domestic violence."

Ignoratio elenchi is the logical fallacy committed when attempting to refute a claim by attacking a different claim. Of course, attacking a completely unrelated claim is unlikely to fool anyone, so in practice the attacked claim is usually similar enough to the target to be confused with it. Presumably, that's what happened in this case, that is, the evidence cited by Lemon was similar enough to Zorza's claim that she was fooled into thinking it was relevant.

As a matter of fact, not only are the three pieces of evidence cited by Lemon irrelevant to Zorza's claim, but they actually undermine it. Since the set of women visiting emergency rooms as a result of violence is a subset of the set of all women visiting emergency rooms, the percentages given in the three claims are fractions of a fraction. According to Sommers, only a small percentage of women visiting emergency rooms are there because of violence, so that Zorza's numbers are in fact much too high, which was Sommers' original criticism. It's not often that one comes across an argument so bad that its premisses not only don't support its conclusion, but actually show it to be false.

The 2nd Puzzle of the Terrorist Acquaintance Solution: Yes, a terrorist is acquainted with a non-terrorist. There are a couple of ways to see this:

  1. Suppose that a terrorist is not acquainted with a non-terrorist. Then whoever is acquainted with Subject Z, who is not a terrorist, cannot be a terrorist either; call this person "Subject Y". A similar line of reasoning applies to Subject Y. It should be obvious that we can carry on this line of reasoning all the way back in the chain of acquaintances until we arrive at the first link, Subject 1. So, Subject 1 can't be a terrorist; yet we know that Subject 1 is a terrorist. Therefore, our assumption is false, which means that a terrorist is, in fact, acquainted with a non-terrorist.
  2. Suppose that the conclusion holds for every chain of n acquaintances, that is, if we have a chain of n people related by acquaintanceship such that the first link in the chain is a terrorist and the last is not, then it follows that at least one terrorist in the chain is acquainted to a non-terrorist link. Now, suppose that we have a chain of n+1 acquaintances such that the first is a terrorist and the n+1st is not. Either the nth link in the chain is a terrorist or not. If link n is a terrorist, then a terrorist is acquainted with a non-terrorist, since link n is acquainted with link n+1. So, suppose that link n is not a terrorist. Then, consider the chain of acquaintances from link 1 to link n: this is a chain of n links such that the first link is a terrorist and the last is not. Thus, by the hypothesis about n-length chains, at least one terrorist link is acquainted with a non-terrorist in the chain. Since this chain is part of the n+1-length chain, it follows that the longer chain also has at least one terrorist acquainted with a non-terrorist.

    In the previous puzzle, we saw that a four-link acquaintance chain whose first link is a terrorist and last is a non-terrorist will have a terrorist acquainted with a non-terrorist. From the above argument, it follows that a five-link chain will also contain a terrorist/non-terrorist acquaintanceship. Similarly, a six-link chain will also have a terrorist acquainted with a non-terrorist, and so on. Therefore, any chain of acquaintances that begins with a terrorist and ends with a non-terrorist will have a terrorist/non-terrorist acquaintanceship.

The first argument is a reductio ad absurdum which is a standard type of argument in logic and mathematics. The second uses mathematical induction, another standard tool of logic and mathematics. Despite its name, mathematical induction is a deductive form of argument.

This puzzle is a generalization of the first puzzle of the terrorist acquaintance, since it shows that the property proven for a chain of four acquaintances holds for an acquaintance chain of any length. Moreover, the relation in the puzzle needn't be acquaintanceship―or looking, from the original puzzle; nor must the property be being a terrorist―or being married, from the original puzzle. The result holds for any chain of things related by a relation, R, such that the first link in the chain has a property, P, and the last lacks it. Given such a chain of any length, we can conclude that there is a link in the chain, x, and a link, y, such that x has P, y does not have P, and x bears R to y.

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