Vagueness, Ambiguity, and Definition

Copyright 2007 Makoto Suzuki

Aims

Distinguish ambiguity and vagueness. Introduce the informal fallacies of

clarity and the fallacy of confusing necessary and sufficient conditions.

Introduce a few conditions for good definitions.

Ambiguity and Vagueness An expression is ambiguous if and only if it

has several non-overlapping meanings. The expression can be a word, phrase,

sentence, paragraph or a whole literary work.

We need to distinguish ambiguity from vagueness.

A term is vague if and only if there are cases in which it is unclear whether or not the term applies. A vague term is not ambiguous as far as it

fails to have two or more distinct meanings.However, many terms are both vague and

ambiguous.

Vagueness A term is vague just in case there are cases in which it is

unclear whether or not the term applies. Some term is vague because there are borderline areas

in a continuum, where it is unclear whether or not the term applies.E.g., “little,” “close,” “new,” “young,” “fat,” “wealthy,”

“thick” and many color terms.Take “young.” Teenagers are young. 50 year-old men

are not young. But are 30 year-old men young? Other term is vague because there are several criteria

for application of the term with no standard of how many of the criteria need be fulfilled and to what degree. E.g., “philosophy,” “religious (person),” “resident,”

“adult” and “tree.”

Vagueness in the second way: An Example: “Religious”

Criteria for being religious include: attending services; belief in a supernatural being; membership in an organized religion; adoption of a set of values upheld by a religion; performance of acts of devotion or piety; and, a sense of reverence (toward, e.g., living things or the

universe). It is unclear whether the term ‘religious’ is applicable to

someone who fulfills only some of the criteria just to some extent. This fact makes the term “religious” vague.

Two Types of Ambiguity

An expression is ambiguous if and only if it has several non-overlapping meanings.

Some sentence is ambiguous because it contains a word or phrase that has two distinct meanings.

Other sentence is ambiguous not because of the ambiguity of any particular term or expression, but because of its grammatical structure. This type of ambiguity is called amphiboly.

Ambiguity of a Term or Phrase

As you see in an English dictionary, many English terms are ambiguous. Ex. “lie” as a verb to mean being in a horizontal

position and not standing or sitting; and “lie” as a verb to mean saying something which he or she knows is untrue.

(The ambiguity of a term is often used in jokes.) In order to have the audience understand and

evaluate the argument properly, the arguer should make clear which meaning of an ambiguous term he or she is using.

Amphiboly (Grammatical Ambiguity): Example 1 “The guard and prisoners who refused

to join in the prison break were tied.” This sounds as if there were guards

who refused to break out of prison. To avoid this type of unclarity, you

should put commas or modifiers properly. In this case, you should put commas like this:“The guard, and prisoners who refused

to join in the prison break, were tied.”

Amphiboly (Grammatical Ambiguity): Example 2

“All Japanese are not ninjas.” This sentence has either of the two distinct readings:

All Japanese are non-ninjas. (narrow scope)• i.e., No Japanese is a ninja.

Not all Japanese are ninjas. (wide scope)• i.e., Some Japanese are non-ninjas.

(The first can be false even if the second is true.) Negation can take narrower or wider scope. In giving an argument, you should avoid “all … not”

construction for the sake of clarity.

Fallacies of Clarity: 1. The Fallacy of Equivocation

The fallacy of equivocation occurs when the seeming plausibility of an argument depends on a word or phrase having two distinct meanings. Examples:

Any law can be repealed by the legislative authority.

Therefore, the law of gravity can be repealed by the legislative authority.

No child should work.

Every person is a child of someone.

Therefore, no one should work.

Caution

Is the following argument a fallacy?A building of Chase Bank stands on the

bank of Duck Lake. Therefore, there is a building of a bank on the bank of Duck Lake.

This argument uses one expression “bank” in two ways, but it is not a case of the fallacy of equivocation.

Merely using one expression in more than one way in an argument does NOT constitute the fallacy of equivocation.

Caution (Continued) For an argument to be a case of the fallacy of

equivocation, its apparent plausibility must depend on using one phrase in more than one way.

The argument in the last page really establishes the conclusion, and its plausibility does not depend on the ambiguity of an expression “bank.” Therefore, it is not a case of the fallacy of equivocation.

In the fallacy of equivocation, if an ambiguous expression in premises is understood in one and the same way throughout, some premise either fails to support the intended conclusion or turns out to be dubious. (Check the examples.)

Fallacies of Clarity: 2. The Fallacy of Amphiboly

The fallacy of amphiboly occurs when the seeming plausibility of an argument depends on an ambiguity in the grammatical structure of a sentence.

Examples: Rural people call the evening meal supper and urban people

dinner.

Therefore, we must arrest those rural people for cannibalism before they eat up any more urban people.

This contract says that the builders expect the sum of $500.00 before and after the completion of the project.

So, we’ll give them $50 before they start and $450.00 after the project is completed.

More Examples (Scope Fallacies)

If James is going to kill Smith, James should kill him gently. James, an assassin, is going to kill Smith. Therefore, James should kill Smith gently.The 1st sentence is true only if it means “It

should be the case that if James is going to kill Smith, James kills him gently.” (wider scope)

This premise combined with “James is going to kill Smith” does not entail that James should kill Smith gently.

Auxiliary verbs like can, must, ought, should, have to etc. can take narrower or wider scope.

Continued Everyone loves someone.

So, someone is loved by everyone. The 1st sentence is true only if it means “For everyone, there

is someone he or she loves.”• “Everyone” takes wider scope, “someone” takes narrower

scope.But the 2nd sentence means “There is someone everyone

loves.”• “Someone takes wider scope, “everyone” takes narrower

scope. Quantifiers like every, all, some, none, only etc. can take

narrower or wider scope.

Caution Merely containing a grammatically ambiguous sentence does not

constitute the fallacy of amphiboly. Distinguish

amphiboly (as a type of ambiguity); and, the fallacy of amphiboly as a fallacious argument based on

amphiboly. For an argument to be a case of the fallacy of amphiboly, its

seeming plausibility must depend on ambiguity in grammatical structure of the sentence(s).

In the fallacy of amphiboly, if the grammatical structure of premises is interpreted in one and the same way throughout, some premise either fails to support the intended conclusion or turns out to be dubious.

Try Question 3, 8 and 11 on p.28

A Role of Definition

Because many words and phrases are ambiguous and value, we often need to define them to make an argument clearly understood.

There are several criteria for good definitions. We will study some of them below.

1. A definition should not be unnecessarily unclear or hard to understand Because we are trying to make the

meaning of a word or phrase clear and understood, an unclear or hard-to-understand definition is problematic.

Problematic examples: “Desire” is the actual essence of man, in

so far as it is conceived, as determined to a particular activity by some given modification of itself. (Spinoza)

“Rectangle” is my favorite geometric figure.

2. A definition should not beg the question: Two Don’ts

First, a definition should not be circular.A problematic example: “Full-time student” means “a

person who is enrolled full time in school.” Such a definition do little to convey what a phrase means. Second, a definition should not prejudge an empirical,

evaluative, or philosophical question.A problematic example: “Vitamin C” is a compound

found in citrus fruits and green vegetables and can prevent you from getting cold.

Another problematic case: “Abortion” means “the justified killing of a non-person in a woman’s womb.”

You cannot make your empirical, evaluative or philosophical view true by definition. You need reasons to show that your views are correct.

3. A definition should provide a necessary and sufficient condition of what you mean. If you cannot give such a definition,

you should explicitly state that you are not trying to give one.

To understand this requirement, you need to know the distinction between a necessary condition, a sufficient condition, and a necessary and sufficient condition.

Let me explain the distinction.

Necessary v. Sufficient Conditions

X is a necessary condition for Y if and only if X must occur in order for Y to occur.i.e., you cannot have Y without X.

X is a sufficient condition for Y if and only ifY must occur if X occurs.

i.e., you cannot have X without Y. As you see, whenever one thing A is a necessary

condition for another thing B, B is a sufficient condition for A; and,

whenever one thing C is a sufficient condition for another thing D, D is a necessary condition for C.

Necessary vs Sufficient

Being a member of B is a sufficient condition for being a member of A.

A

B

Being a member of A is a necessary condition for being a member of B.

Necessary and Sufficient Condition

X is a necessary and sufficient condition for Y if and only if

X is both a necessary condition and a sufficient condition.

i.e., both X must occur in order for Y to occur, and Y must occur in order for X to occur – X and Y must go together on every occasion.

Test yourself: Necessary v. Sufficient Conditions

The presence of water is a condition for it to rain.

Being a plane closed figure is a condition for being a triangle.

An object being red is a condition for the object being colored.

An object being a BMW is a condition for the object being a car.

An argument’s having all true premises and being valid is a condition for being a sound argument.

necessary

necessary

sufficient

sufficient

necessary and sufficient

A Definition and A Necessary Condition

“Bird” means “feathered animal that can fly”

What is wrong with this definition? “Bird” then does not apply to penguins,

kiwis, ostriches, and cassowaries. This means that the definition fails to state

a necessary condition for being a bird.

A Definition and A Sufficient Condition

“Scissors” means “an instrument for cutting”.

What is wrong with this definition?

It applies to knives. This definition fails to give a

sufficient condition for being scissors.

A Definition, A Necessary Condition, and A Sufficient Condition “Bird” means “animals that can fly”. What is wrong with this definition? It does not apply to penguins, kiwis,

ostriches, and cassowaries.It fails to state a necessary condition

for being a bird. It applies to bats and certain insects.

It fails to state a sufficient condition for being a bird, too.

Summary

1. A definition should not be unnecessarily unclear or hard to understand.

2. A definition should not beg the question: A definition should not be circular; and, A definition should not prejudge an empirical,

evaluative, or philosophical question.

3. A definition should provide a necessary and sufficient condition of what you mean.

If you cannot give such a definition, you should explicitly state that you are not trying to give one.

The Fallacy of Confusing Necessary and Sufficient Conditions

This fallacy is committed when apparent plausibility of an argument depends on confusing a necessary condition and a sufficient condition.

Examples

Donna, you said if I wanted to bake a good, light soufflé, I had to use fresh eggs. That’s exactly what I did. But my soufflé was heavy and tasteless. I ruined my dinner party. I’ll never listen to you again.

Professor, you said that I will not get an A in the course unless I get an A on the final. And that’s exactly what I did. So, you lied. You gave me a B. I’m going to protest this.

Exercise on p.24

Jokes Using the Ambiguity of a Term: An Example

In the Mel Brooks’ movie Young Frankenstein, Dr. Frankenstein arrives at his family’s castle in Transylvania and, as he is lifting his assistant Inga out of their carriage, notices big elaborate knockers on the door.

He exclaims: “What knockers!” Inga, thinking he is complementing her,

replies “Oh, thank you Doctor” with an excited smile.