3.6.2: How to Avoid Errors when Creating Definitions
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Let's turn now from examining the purposes and kinds of definitions to the more important topic of avoiding errors in definitions. Here is a faulty lexical definition:
By definition, a square is a four-sided, plane, closed geometrical figure in which all angles are 90 degrees.
Did you notice the problem? The definition permits too many things to be called squares. It lets in any rectangle. So we say it is too broad. The same kind of error is made when vegetable is defined as a food that is not a fruit.
Here is the opposite kind of error:
By definition, a triangle is a three-sided, plane, closed geometrical figure with equal sides.
This definition rules out triangles that don't have equal sides, so it is too narrow. Both kinds of errors would be committed at the same time if someone were to define a vixen as a young fox. The definition is too broad because it permits young male foxes to be vixens. It is too narrow because it rules out old female foxes.
Is the following proposed definition too broad, too narrow, or both? Why?
Science: The study of geology, biology, chemistry, or physics.
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It is too narrow because it leaves out biochemistry and astronomy.
Ambiguous definitions and overly vague definitions are two other faults in constructing definitions. Suppose you did not know the meaning of the slang term put down, and I defined it this way:
By definition, a put down is a shot intended to harm.
If you didn't know that a put down is something done verbally, you might be misled into thinking that it is something that can be done with a pistol. So, the definition suffers from ambiguity.
Definitions by example are always vague. Defining dog in terms of a dog's genetic makeup would be less vague and better biology than defining it as something like a collie. Figurative language in a definition always produces an overly vague definition. That would be the problem if we defined dog as "man's best friend" or defined president of a country as "pilot of the ship of state." Science and mathematics have progressed in part by carefully avoiding imprecise definitions whenever possible.
Scientific definitions are usually overly complex for the nonscientist. Hoping to learn how to distinguish a spider from other bugs, the nonscientist might ask a biologist to define spider. If the biologist gave a definition that referred to the spider's genetic code, the definition would fail to elucidate. That is, it wouldn't get the point across.
Defining dog for a third grader by giving several examples would be vague, but appropriate. After all, we give definitions in order to achieve the purpose of getting the meaning across to others. If we achieve our purpose, that is all that counts, vagueness or no vagueness.
Failure to convey the grammatical category is also a source of error. If the audience doesn't know the grammatical category of the term lassitude, then defining it as "when you feel very tired" could mislead an unwary member of the audience into supposing that the definition could be substituted this way:
Monroe's lassitude got him fired, so
Monroe's when you feel very tired got him fired.
Suppose someone had never heard the word nigger, and you defined it for them as "black person." By covering up the negative connotation, you would have been offering a faulty definition that could get the user in trouble. So, failure to convey the term's connotation is the type of error here. It could be corrected by defining nigger as "derogatory term for persons with black skin."
Another way that a definition can fail is by being circular. The author of a circular definition makes the mistake of improperly using the term that is supposed to be defined. For example, the person who defines apprentice as "someone who is an apprentice to a laborer" is not informing anybody of anything other than the grammatical category of apprentice.
Circularity can also be a problem with a chain of definitions, even if no single definition in the chain is itself circular. Here is an example:
Effect is that which is produced by a cause.
Cause is that which produces an effect.
Another kind of error in the definition process occurs in the following pair of definitions:
An airline stewardess is a woman who provides service to airline passengers during flight.
An airline steward is a male airline stewardess.
This is an inconsistent definition because it implies that a steward is both male and female. To remove the gender identification of steward and stewardess, airlines at the end of the twentieth century began recommending use if the genderless term flight attendant. Usually it is not important, and is even sexist, to identify the sex of a worker or occupation. That's the main reason that the term mailman is dying out, to be replaced by postal carrier.
When someone gives the lexical definition of atheist as "non-Christian," the error is to give a definition that
a. commits an attack on the arguer, not the argument.
b. is too broad.
c. is too narrow.
d. is circular.
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Answer (a)
Errors in operational definitions are especially hard to avoid. The problem is really to minimize the degree to which the class of things identified by the operational definition deviates from the class identified by the lexical definition. For instance, suppose some scientists report that
American homes are neater now than they were in 1900.
Before you accept the scientists’ claim, ask yourself how the term neater was operationalized. A good reporter would provide the reader with the actual operational definition. A reader not given this information would have to worry that the term was operationally defined by counting the number of objects in the house; the fewer objects, the neater the house. That definition is both too narrow and too broad and thus isn't true to the lexical definition of neat that you use. Readers should put less faith in a scientific report if they can't be satisfied that an important term was adequately operationalized.
What is the main flaw in this set of definitions?
Vague means "suffering from vagueness."
Vagueness means "the result when vague words are used."
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Circularity
One final reminder about definitions: they serve several purposes, not just making meaning more precise, or accurately reporting the common meaning. For example, let me define “minor back surgery.” It is back surgery on someone else.