The following are fallacies of ambiguity:

• Equivocation: the same term is used in two different ways
• Amphiboly: the structure of a sentence allows two different interpretations
• Accent: an emphasis suggests a meaning different from what is actually said

The fallacies in this section are all cases where a word or phrase is used unclearly. There are two ways whereby this may occur:

1. The word or phrase may be ambiguous, in which case it has more than one distinct meaning.
2. The word or phrase may be vague, in which case it has no distinct meaning.

1. Equivocation:

The same word is used with two different meanings.

Examples:

1. The sign said, "Fine For Parking Here," and since it was fine, I parked there.
2. All murderers are inhuman. Thus, no murderer is human. (From Barker, p. 164; this is called "illicit obversion.")
3. Criminal actions are illegal, and all murder trials are criminal actions. Thus all murder trials are illegal. (Here the term "criminal actions" is used with two different meanings. Example borrowed from Copi.)
4. A plane is a carpenter's tool, and the Boeing 737 is a plane. Hence the Boeing 737 is a carpenter's tool. (Example borrowed from Davis, p. 58)

Convincing Others: Identify the word which is used twice. Then show that a definition which is appropriate for one use of the word would not be appropriate for the second use.

References: Barker: 163; Cedarblom and Paulsen: 142; Copi and Cohen: 113; Davis: 58

2. Amphiboly:

An amphiboly occurs when the construction of a sentence causes it to have two different meanings.

Examples:

1. Last night I shot a burglar in my pajamas.
2. Save soap and waste paper. (From Copi, p. 115)
3. The Oracle of Delphi told Croseus that if he pursued the war he would destroy a mighty kingdom. (What the Oracle did not mention was that the kingdom he would destroy would be his own. Adapted from Heroditus, The Histories.)

Convincing Others: Identify the ambiguous phrase and show the two possible interpretations.

Reference: Copi and Cohen: 114

3. Accent

Emphasis is used to suggest a meaning different from the actual content of the proposition.

Examples:

1. It would be illegal to give away Free Beer!
2. The first mate, seeking revenge on the captain, wrote in his journal, "The Captain was sober today." (He suggests, by including the word, "today," that the Captain is usually drunk. From Copi, p. 117)

Convincing Others: Show how changing the emphasis changes the interpretation.

Reference: Copi and Cohen: 115

The term, "non sequitur," literally means "it does not follow." In this section we describe fallacies which occur as a consequence of invalid arguments.

The following fallacies are non sequiturs:

• Affirming the Consequent
• Denying the Antecedent
• Inconsistency

1. Affirming the Consequent:

Any argument of the following form is invalid:

• If A then B
• B
• Therefore, A

Examples:

1. If I am in Calgary, then I am in Alberta. I am in Alberta. Thus, I am in Calgary. (Of course, even though the premises are true, I might be in Edmonton, Alberta.)
2. If the mill were polluting the river, we would see an increase in fish deaths. And fish deaths have increased. Thus, the mill is polluting the river. (The fish deaths might be caused by pesticide run-off, and not the mill.)

Convincing Others: Show that even though the premises are true, the conclusion could be false. In general, show that B might be a consequence of something other than A.

References: Barker: 69; Cedarblom and Paulsen: 24; Copi and Cohen: 241

2. Denying the Antecedent:

Any argument of the following form is invalid:

• If A then B
• Not A
• Therefore, not B

Examples:

1. If you get hit by a car when you are six, you will die young. But you were not hit by a car when you were six. Thus you will not die young. (Of course, you could still be hit by a train at age seven, in which case you still die young.)
2. If I am in Calgary, then I am in Alberta. I am not in Calgary. Thus, I am not in Alberta.

Convincing Others: Show that even though the premises are true, the conclusion may be false. In particular, show that the consequence B may occur even though A does not occur.

References: Barker: 69; Cedarblom and Paulsen: 26; Copi and Cohen: 241

3. Inconsistency:

The author/speaker asserts more than one proposition in such a way that the propositions cannot all be true.

Examples:

1. Montreal is about 200 km from Ottawa, while Toronto is 400 km from Ottawa. Toronto is closer to Ottawa than Montreal.
2. John is taller than Jake, and Jake is taller than Fred, while Fred is taller than John.

Convincing Others: Assume that one of the statements is true, and then use it as a premise to show that one of the other statements is false.

Reference: Barker: 157

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