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June 30th, 2010 (Permalink)

The Third Puzzle of the Unmatched Socks

Three other men worked for the same company but shared a different office: Mr. Brown, Mr. Green, and Mr. Brown-Green. Today, when they came to work, one was wearing brown socks, another green socks, and the third unmatched socks: one brown and one green. Again, the men were not wearing socks of colors that matched their names. At the same time, each man wore long trousers that hid his socks, so that no one could see what color socks he was wearing. If you could enter the office, pull up only one trouser leg on just one of the men and see what sock he wore on that leg, could you determine what color of socks each man wore? Whose trouser leg would you pull up?


June 29th, 2010 (Permalink)

The Second Puzzle of the Unmatched Socks

The next day, the three men were back in the office, again with sock colors that did not match their names. Now, however, one of them was wearing black shoes, another grey shoes, and the third white ones. Like their socks, the colors of their shoes did not match their names. Not only that, but the colors of their shoes did not match that of their socks. In addition, nobody wore white socks with black shoes.

What color combination of shoes and socks was each man wearing?


June 28th, 2010 (Permalink)

The Puzzle of the Unmatched Socks

Three men―Mr. Black, Mr. Grey, and Mr. White―work in the same office. Today, one of them wore black socks to work, another wore grey socks, and the third wore white socks.

"That's strange", Mr. Black remarked to the man wearing grey socks, "none of us is wearing socks of a color that matches our names!"

What color of sock was each man wearing?


June 25nd, 2010 (Permalink)

Name That Fallacy, Too!

…40 states not only donít ban handguns―they allow citizens with permits to carry [handguns] concealed in public. … Crime went down in those states. And after Chicago passed its ban in 1983, crime went up. Crime never returned to pre-ban levels.


In the article from which the quote above was taken, John Stossel also tells the story of an elderly Chicago man who used an illegal handgun to kill an armed robber who had broken into his house. I can't really blame Stossel for recounting this story, as it's standard journalistic practice to use anecdotes to enliven dull policy stories. However, it would be just as easy to find a case of a child using an illegal handgun to shoot a sibling, or some similar tragedy, and that's what an anti-handgun journalist would do. A single anecdote is poor evidence, whether it's used for or against restrictions on gun ownership. For this reason, the story is at least a logical boobytrap for the anecdotal fallacy.

Stossel presents Mayor Daley's response to the incident as if it were somehow wrong or insensitive, but it's reasonable for the mayor to reject it as evidence of anything. (Of course, I don't mean to defend Daley's behavior at an apparently unrelated press conference.) Similarly, it would be reasonable for Stossel to reject a story of a child accidently killed by a sibling with an illegal handgun as evidence that handguns should be banned. "It's a tragedy", he could say, "but in the long run access to guns saves far more innocent lives than are lost." Daley may be wrong, but one anecdote and some post hoc reasoning don't show it.

Source: John Stossel, "Why Chicagoans Need Guns", John Stossel's Take, 6/23/2010

June 22nd, 2010 (Permalink)

Name That Fallacy!

Data from the U.S. Federal Bureau of Investigation show that America has been on a firearms buying spree since the end of 2005. Meanwhile, the FBI recently released preliminary 2009 crime data indicating that violent crime has been dropping at an accelerating rate since the end of 2006. The FBI reports the number of background checks, by month, requested for potential firearms purchases through licensed dealers. When a prospective buyer wants to buy a gun, he fills out a form which the dealer submits to law enforcement. If approved, the sale proceeds. This system is called the National Instant Criminal Background Check System, or NICS for short. …[A]fter gun sales attained record growth in 2006, violent crime rates began to fall in 2007. As gun sales continued to register records each following year, violent crime rates decreased at an accelerating rate.

More guns, less murder

…[L]ike overall violent crime, after gun sales began to peak in 2006, the murder rate declined at an accelerating pace beginning in 2007….

More guns, less rape, robbery, and aggravated assault

…[A]fter NICS requests attained 10% annual growth during the 2006-2009 period, crime rates for all four FBI major violent crimes began to decrease, generally at accelerating rates. Is this because criminals know more people have been buying guns and getting concealed carry permits? … More guns. More gun owners. More law-abiding citizens carrying handguns in public. More caution amongst violent predators? … The numbers speak louder than anti-rights rhetoric: more guns, less crime.


Source: Howard Nemerov, "FBI Crime Stats Show an Armed Public Is a Safer Public", Pajamas Media, 6/3/2010

June 20th, 2010 (Permalink)

New Baggini

Julian Baggini, author of The Duck that Won the Lottery, has a new book coming out called Do They Think You're Stupid?: 100 Ways of Spotting Spin and Nonsense from the Media, Celebrities and Politicians. I think the title question is rhetorical.

He also has an article for the BBC (see the Source, below), which I guess is taken from the book, about misperceptions of risk and placing an economic value on a human life. Read the whole thing, but I want to comment, specifically, on his remark that "people are much more risk averse when it comes to plane travel than they are to driving their own cars."

I think a major source of this discrepancy is the anecdotal fallacy: When a large airplane crashes, people die in double or triple digits, and the tragedy is extensively covered by the national, and even international, news media. In contrast, with rare exceptions, car wrecks kill people in single digits, and the accident will be covered by the local news at best, unless a victim is a celebrity. As a result, people have an exaggerated sense of the risk of flying as opposed to that of driving.

Of course, this same effect is part of the reason why flying is so much safer than driving. For example, as Baggini points out, the restrictions placed on flying in Europe due to the volcanic eruption are more stringent than would be tolerated for road travel. As a consequence, the number of lives saved from plane crashes may be surpassed by the number lost in car wrecks when people switch to the less safe form of travel.

Source: Julian Baggini, "Is driving more dangerous than flying through ash?", BBC News, 4/21/2010

June 17th, 2010 (Permalink)


Q: Regarding the tu quoque fallacy: often in politics you will hear something like the following:

Arguer 1: "President Obama did such and such."

Arguer 2: "Oh yeah, well, President Bush did such and such as well."

In other words, often in politics people will ignore accusations and simply attack the other politician. Could something like this be considered a tu quoque fallacy, even though the politicians are being referred to by third parties? In other words, it is a sort of tu quoque in the sense that Arguer 2 is saying "your politician too." The response by Arguer 2 is irrelevant to the issue brought up by Arguer 1. If this is not considered a tu quoque, what fallacy would it be?―Aaron Brake

A: You're right to notice a similarity in this type of argument to the Tu Quoque Fallacy. However, strictly speaking, a tu quoque argument is a criticism turned back on the critic: person 1 criticizes person 2 for a fault and 2's defense is to accuse 1 of the same fault: "tu quoque" means "you, too!"

In the type of argument in question, person 1 criticizes person 3 for a fault and 2 defends 3 by making the same criticism of person 4. Of course, persons 3 and 4 aren't just some randomly-selected passers-by, but there's presumably some relationship between persons 1 and 4 and between 2 and 3. In the example, 1 politically supports 4 while 2 supports 3. Even so, this doesn't have the same form as a true tu quoque. The name, however, is not so important; what's important is understanding the type of argument it is and what's wrong with it.

This is a case where I think that the taxonomic relationships between fallacies are helpful, in particular, the subfallacy relationship. If an example seems similar to a particular fallacy, but doesn't exactly fit, then check the Taxonomy for closely-related fallacies.

In this case, Tu Quoque is a subfallacy of Two Wrongs Make a Right, which I think is the key to understanding where the example goes wrong. The fact that President 43 did something bad in no way excuses President 44 from committing the same error. On the contrary, 44 should've known better! 43 may have had the excuse of ignorance, but 44 lacks that excuse.

Defending 44 by attacking 43 is just a way of changing the subject―that is, a Red Herring. Again, the Taxonomy shows this relationship, since Two Wrongs is a subfallacy of Red Herring. Of course, attacking 43 may be a rhetorically effective distraction if the original critic is a fan of 43, just as Tu Quoque is an effective way of changing the subject since people usually feel the need to defend themselves when criticized. Similarly, political partisans may feel called upon to defend presidents of their own party, which is why this is such a distracting―and common!―tactic in political debates.

In sum, I'm satisfied with saying that the argument is a type of Two Wrongs Make a Right. However, if you want to give it a more specific name, I like "Tu Quoque by Proxy".

June 10th, 2010 (Permalink)

Think, don't Blink!

That's the message of an interesting article about intuition in The Chronicle of Higher Education by psychologists Daniel Simons and Christopher Chabris (S&C), the authors of the new book The Invisible Gorilla, and Other Ways Our Intuitions Deceive Us. Go read the whole thing, then come back and read this whole thing!

The title of S&C's book The Invisible Gorilla refers to studies of what is called, rather pompously, "inattentional blindness", which just means that people sometimes don't notice things when they are paying attention to something else. However, it can be quite surprising what you fail to notice, as is shown by the "invisible gorilla" video.

Apparently, psychologists have just discovered this phenomenon, but magicians have known and used it for thousands of years: they call it "misdirection". I've long thought that psychologists would benefit from reading philosophers and logicians so that they weren't continually rediscovering things that Plato and Aristotle knew. However, they could also learn a lot from magicians, who have centuries of practical knowledge of human psychology, especially involving perception, attention, and illusions both perceptual and cognitive.

S&C seem to lump together a lot of different phenomena under the heading of "intuition". For instance, the examples involving possible art forgeries involve pattern recognition, that is, someone who knows an artist's style either recognizes a work as genuine, or suspects that it is a forgery. This is like suddenly recognizing the face of an old friend after a separation of many years: something seems to just "click" in your head and you can put a name to the face. However, it's intuition only in the sense that it's fast and you can't describe the process involved, since it doesn't occur in conscious thought. Anyone who has spent any time looking at art will soon learn to recognize an artist's style―at least, if the artist has a recognizable style. However, it is that style that a forger attempts to imitate, so we may experience the same "flash" of recognition when we see a good forgery as we get from the real thing.

The kind of thinking that uses rules of thumb seems to be "intuitive" only in its speed: it's faster to take a shortcut than to follow out a long train of thought. However, unlike the case of pattern recognition, when we reason with rules of thumb we're still reasoning, no matter how fast.

Of course, the part of the article most relevant to logical fallacies is the discussion of mistakes made in thinking about cause and effect, and there we meet up with a few old friends. I hope that you experienced a few flashes of recognition as you read it, and I'll leave it to you to put names to those familiar faces. Again, I'm doubtful about calling fallacious causal reasoning "intuition" just because it relies on quick-and-dirty rules of thumb.

All of this illustrates the vagueness and ambiguity of the word "intuition". Philosophers and logicians tend to use the word with the meaning of an unconsidered judgment, that is, an intuition about something is the first thought that pops into your head before you've had a chance to think about it. That first thought might be right but, then again, it might not be, and how will we ever know if we don't think about it?

I haven't read Malcolm Gladwell's book Blink, which is apparently the target of S&C's ire, but I share their skepticism about any celebration of the value of snap judgments. Perhaps Gladwell is responsible for lumping together pattern recognition, introspection, and cognitive shortcuts as "intuition". Such rapid decision-making certainly has its place, namely, when time is of the essence, but it should be kept in that place. When there's time to think things through, we should take the time to think, not blink.

Source: Daniel J. Simons & Christopher F. Chabris, "The Trouble With Intuition", The Chronicle of Higher Education, 5/30/2010

June 7th, 2010 (Permalink)


Cricket sex video reveals wild mating behavior

Cricket sex? What's next, rugby sex?

Solution to the Puzzle of the Unmatched Socks: Mr. Black has on white socks, Mr. Grey black socks, and Mr. White grey ones.

Mr. Black cannot be wearing black socks, since those would match his name, and he can't be wearing grey socks, because he spoke to the man who wore grey ones. Therefore, Mr. Black is wearing white socks. Mr. Grey can't have on white socks, since Mr. Black is wearing those, and he can't wear grey ones, because those would match his name. So, Mr. Grey has on black socks. That leaves the grey socks for Mr. White.

Source: Martin Gardner, The Snark Puzzle Book (1990), p. 89.

Solution to the Second Puzzle of the Unmatched Socks: The three men have on the same color socks as before. In addition, Mr. Black has on grey shoes, Mr. Grey wore white shoes, and Mr. White black ones.

Mr. Grey can't wear either grey socks or shoes, since those would match his name. So, he's wearing either black shoes with white socks or white shoes with black socks. Since no one wears white socks with black shoes, it follows that Mr. Grey is wearing white shoes and black socks. Therefore, Mr. White must have on grey socks, because he can't match his name by wearing white ones, and Mr. Grey is wearing the black ones. Since Mr. White can't wear white shoes, which would match his name, or grey ones, which would match his socks, he must be wearing black shoes. That leaves grey shoes and white socks for Mr. Black.

Solution to the Third Puzzle of the Unmatched Socks: You should pull up Mr. Brown-Green's trouser leg―it doesn't matter which leg―and check out the color of his sock. From that color you can deduce the colors of each man's socks in the following way:

Since the colors of the socks the three men wear do not match their names, Mr. Brown-Green is not wearing the mismatched pair of brown and green socks, which means that he is wearing either the brown socks or the green socks. So, if you see a brown sock, he's wearing the brown socks; if you see a green sock, he has on the green ones.

Let's suppose that you see a brown sock; then, Mr. Brown-Green is wearing the brown socks. Since Mr. Green can't wear the green socks without matching his name, he must be wearing the mismatched pair. That leaves Mr. Brown wearing the green socks. If you see a green sock, the reasoning is similar, but leads to the conclusion that Mr. Brown-Green is wearing the green socks, Mr. Brown the mismatched pair, and Mr. Green the brown ones.

So, in either case, you can determine what color of socks each of the three men is wearing simply from a glimpse at one of Mr. Brown-Green's socks. However, this reasoning won't work when applied to the other two men, since you won't be able to tell from a single sock whether the man is wearing socks of the same color or not.

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