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February 24th, 2007 (Permalink)

Check it Out

Tim van Gelder, of Critical Thinking on the Web, has a new weblog concentrating on argument mapping, but his latest entry is a list of books for improving critical thinking skills. I second his inclusion of the Cialdini, Heuer, and Piattelli-Palmarini books. It's been a long time since I looked into Giere's book, but my impression of it is favorable. I've also read some of Merrilee Salmon's text, but not enough to recommend it. I've seen Gerry Spence's book, but since he is a celebrity lawyer―in both senses―I thought that it was probably junk and ignored it. I guess that I'll have to take a look at it, now! I haven't yet read Whyte's book, which is itself a crime against logic. The others I'm not familiar with, so I have some more reading to do!

Source: Tim van Gelder, "Critical Thinking―Where to start?", Rationale Thoughts, 2/24/2007

February 17th, 2007 (Permalink)

Who's an "Average" American?

One can be an American of average height, of average weight, of average intelligence, or of any other quantifiable characteristic. But is an "average American" someone who is average in every such characteristic? If so, there may well be no average Americans.

According to the American Farm Bureau Federation: "In just five weeks, the average American earns enough disposable income to pay for his or her food supply for the entire year…." Apparently, this means an American who has a mean average income spends approximately 10% of that income on food. However, as I've noted here before (see the Resources), mean income is not the best "average" to represent a typical income, since incomes are skewed by very high earners. The median is a better measure of typicality, but appears not to have been available in this case.

Given the statistics it had to work with, the Farm Bureau's claim doesn't appear to be significantly misleading and, as The Numbers Guy points out, Americans in the middle quintile of income spend only about 12 and a half percent of it on food. However, I'm not so sure that "Food Check-Out Day" is a good way to publicize this fact. Why not just say that most Americans spend about 10% of their income on food, give or take a few percent? That seems pretty cheap to me.



February 8th, 2007 (Permalink)

Check 'Em Out

February 5th, 2007 (Permalink)

Get the "Lead" Out

The following sentence is from John Allen Paulos' latest "Who's Counting" column:

Scientific progress is by its nature unpredictable, but some extra [National Cancer Institutes] might also have lead to breakthroughs in cancer treatment.

That should read "led" instead of "lead". "Led" is the past tense of the verb "to lead". I've noticed this mistake recently in several newspaper and magazine articles. Moreover, Sidney Goldberg complained a couple of years ago about this error occurring in the New York Times:

One of the more annoying illiteracies of the Times is its inability to spell the past tense of "to lead." Almost as often as not, the Timesmen spell the past tense as "lead," when "lead" can only be the present tense of "to lead" or the name of the heavy metal. (The past tense of "to lead," of course, is "led.") I don't think a day passes without the Times getting it wrong. For instance, on July 24, the paper published the following: "On Friday, the rebel Shiite cleric Moktada al-Sadr, who lead an uprising…"

Also, I found a few reference books which list "lead"/"led" confusion as a common error, including Precision, a writing handbook by Robert Gula, the author of Nonsense. So, there is some evidence that this mistake is a common one.

Of course, this is a grammatical or spelling mistake rather than a logical one, but I suspect that it's made more likely by the ambiguity of the word "lead" mentioned by Goldberg. The error occurs because it is easy to confuse the past tense of the verb lead spelled and pronounced "led", with the noun lead spelled "lead" but also pronounced "led".

I don't know whether this mistake is growing more common, or I've just started noticing it. Perhaps it's become more common as more writers and editors rely on spell checkers, since this is one that a spell checker won't catch―at least not the one in Microsoft's Word program. One thing that spell checkers should do is free up writers and editors from having to look up the spelling of words in dictionaries; some of that saved time and energy can be devoted to checking for common errors that the spell checker will miss. Here's one to look out for!

Update (2/7/2007): Reader John Olski writes:

You might note that the past tense of read is not "red," but rather "read." The lead-led confusion is more understandable in light of this, and English is often confusing when one has to wait until the end of a sentence in order to interpret the tense of an initial verb:
  • "We read the sports section of the newspaper first each Monday."
  • "We read the sports section of the newspaper first on February 5th, 2007."

Good point, though there's a good reason why the past tense of read should not be spelled "red", since that would create an ambiguity with the word for the color! You're right that a misleading analogy between "read" and "lead" may be a contributing factor in the confusion.


February 3rd, 2007 (Permalink)

Lessons in Logic 2: Statements

When we reason about something, we attempt to determine its truth-value. There are two truth-values: true and false. What we are trying to determine the truth-value of is a statement. A statement is a sentence with a truth-value, that is, it is either true or false.

Example: It is snowing.

Synonym: Proposition

Statements contrast with other types of sentence, such as questions and commands. The distinguishing feature is whether the sentence has a truth-value, for neither questions nor commands are true or false.

Examples: Is it snowing? Let it snow!

Reasoning is constructed out of statements, so the first skill that a budding logician needs to learn is how to recognize statements and to tell them from non-statements.

Exercises: Determine which of the following sentences are statements and which are not.

  1. The first witness was the Hatter.
  2. "Take off your hat," the King said to the Hatter.
  3. Do cats eat bats?
  4. "But what did the Dormouse say?" one of the jury asked.
  5. "Off with her head!"
  6. One of the jurors had a pencil that squeaked.
  7. "You're nothing but a pack of cards!"

    Source: Lewis Carroll, Alice in Wonderland


Previous Lesson: Introduction | Next Lesson: Arguments

February 2nd, 2007 (Permalink)

Blurb Watch

An ad for the new documentary about Ralph Nader, "An Unreasonable Man", carries the following blurb:

A. O. Scott, The New York Times

Here's the context from which this blurb was taken:

[Nader's] impact on these areas of modern life is the focus of the movie’s riveting first hour, which is as much the biography of a movement as the story of a single man.

If you're no longer riveted to your seat after the first hour and you leave early, will the theater refund half your money?


Answers to the Exercises:

  1. Statement
  2. Statement: Don't let the fact that what the King says is a command throw you off; it's either true that the King told the Hatter to take off his hat or it's false, so the sentence is a statement.
  3. Not a statement: It's a question.
  4. Statement: Again, don't be confused by the quoted question; either it's true that one of the jury asked that or it's false, thus it's a statement.
  5. Not a statement: It's a command.
  6. Statement
  7. Statement: Don't be fooled by the exclamation point; this sentence is not a command, but an emphatic statement.

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