3.4: Being Pseudoprecise

The nineteenth-century American writer Mark Twain once said he was surprised to learn that the Mississippi River was 1,000,003 years old. He hadn't realized that rivers were that old. When asked about the "3," he answered with a straight face that three years earlier a geologist had told him the Mississippi River was a million years old. In this case, "1,000,003" is not precise; it is silly. Technically, "1,000,003" is called pseudoprecise. Pseudoprecision is an important cause of fallacious reasoning when quantifying something—that is, putting a number on it.

Definition

A claim is pseudoprecise if it assigns a higher degree of precision than circumstances warrant.

Predicates can pick out properties, as when the predicate “is a blue car” picks out the property of being a blue car. Being old is a vague property; being 77 years old is more precise. Placing a number on some property can improve precision in describing the object. But not always. Placing a number on a property of an object is pseudoprecise if (1) the property cannot be quantified, that is, it doesn’t make sense to put a number on it, (2) the object cannot have the property to that degree of precision, or (3) the object could have the property to that degree of precision but the person is not justified in claiming that much precision.

Let’s consider some examples of this. The Mississippi River story is an example of type 3. A number (1,000,003) is used by a person (Mark Twain) to quantify (measure with a number) some property (age) that an object (the Mississippi River) has. The river could be precisely that old, but Twain was not justified in claiming that much precision. Even the geologist couldn’t know enough to place such a number on the age of the Mississippi.

For an example of pseudoprecision of type 1, suppose you heard that Mark Twain admired Andrew Jackson 2.3 times as much as he admired the previous president, John Quincy Adams. You would be hearing something pseudoprecise, because the precision is a sham. All you can sensibly say about admiration is that some is strong, some is weak, and some is stronger than others. Forget about numbers.

Although quantifying can often improve precision, there is a limit to how precise you can get this way. For example, if you were to read that Napoleon Bonaparte was 5 foot 1.4748801 inches tall, you shouldn't believe it. Measuring people's height doesn't make sense to this many decimal places. Inhaling can raise a person's measured height by tenths of an inch, while taking a bath can lower it by a hundredth. Too precise a height for Napoleon is an example of pseudoprecision of type 2.

If a statistical report mentions that the average size nuclear family in your community has 2.3 children, is this number pseudoprecise? No. The 2.3 statistic is the result of dividing the whole number of children in nuclear families by the whole number of nuclear families. It doesn't imply that any real family has 2.3 children, which would be silly.¹

Exercise \(\PageIndex{1}\)

Which one statement below probably suffers the most from pseudoprecision?

a. There is an average of 1.5 guns in each household in Dallas, Texas.
b. Our company's computer can store 64,432,698,003 characters simultaneously.
c. The first flowering plant appeared on earth nearly 100 million years ago.
d. Today, David used his new precision laser distance-measuring tool and discovered the diameter of the cloud overhead to be 0.4331 times the diameter of the cloud that was overhead yesterday at the same time.
e. The reading head of the computer's magnetic disk is 0.4331 inches from the disk itself.

Answer

Answer (d). Can a cloud be given a width to an accuracy of a ten thousandth of an inch?

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¹ Note that the sentence uses the word imply in the sense of "require." The word imply also can be used in the sense of "suggest," although it usually will not be used that way in this book.