This section describes the following fallacies involving statistical syllogisms:

• Accident
• Converse Accident

A statistical generalization is a statement which is usually true, but not always true. Very often these are expressed using words such as "most," "usually," "generally," etc.

Fallacies involving statistical generalizations occur because the generalization is not always true, but an author/speaker treats it as though it were.

1. Accident:

A general rule is applied when circumstances suggest that an exception to the rule should apply.

Examples:

1. The law says that you should not travel faster than 50 kph. Thus even though your father could not breathe, you should not have traveled faster than 50 kph.
2. It is good to return things you have borrowed. Therefore, you should return this automatic rifle from the madman you borrowed it from. (Adapted from Plato's Republic, Book I).

Convincing Others: Identify the generalization in question and show that it is not a universal generalization. Then, show that the circumstances of this case suggest that the generalization ought not to apply.

Reference: Copi and Cohen: 100

2. Converse Accident

An exception to a generalization is applied to cases where the generalization should apply.

Examples:

1. Because we allow terminally ill patients to use heroin, we should allow everyone to use heroin.
2. Because you allowed Jill, who was hit by a truck, to hand in her assignment late, you should allow the entire class to hand in their assignments late.

Convincing Others: Identify the generalization in question and show how the special case was an exception to the generalization.

Reference: Copi and Cohen: 100

The following fallacies are cases of missing the point:

• Begging the Question: the truth of the conclusion is assumed by the premises
• Irrelevant Conclusion: an argument in defense of one conclusion proves another
• Straw Man: the arguer attacks a weak version of an opponent's argument

These fallacies have in common a general failure to prove that the conclusion is true.

1. Begging the Question: (petitio principii):

The truth of the conclusion is assumed by the premises. Often, the conclusion is simply restated in the premises in a slightly different form. In more difficult cases, the premise is a consequence of the conclusion.

Examples:

1. Since I'm not lying, it follows that I'm telling the truth.
2. We know that God exists, because the Bible says God exists. What the Bible says must be true, since God wrote it and God never lies. (Here, we must agree that God exists in order to believe that God wrote the Bible.)

Convincing Others: Show that in order to agree that the premises are true we must already agree that the conclusion is true.

References: Barker: 159; Cedarblom and Paulsen: 144; Copi and Cohen: 102; Davis: 33

2. Irrelevant Conclusion (ignoratio elenchi):

An argument which purports to prove one thing instead proves a different conclusion.

Examples:

1. You should support the new housing bill. We can't continue to see people living in the streets; we must have cheaper housing. (We may agree that housing is important even though we disagree with the housing bill.)
2. Tom is such an idiot! Yesterday, he tripped over his own dog, and today he can't seem to be able to write small enough to fit everything on an application. He couldn't even read the note that I had left for him. (Tom is probably not an idiot but only needs glasses.)

Convincing Others: Show that the conclusion proved by the author is not the conclusion that the author set out to prove.

Reference: Copi and Cohen: 105

3. Straw Man:

The author attacks an argument which is different from, and usually weaker than, the opposition's best argument.

Examples:

1. People who opposed the Charlottown Accord probably just wanted Quebec to separate. But we want Quebec to stay in Canada.
2. We should have conscription. People don't want to enter the military because they find it an inconvenience. But they should realize that there are more important things than convenience.

Convincing Others: Show that the author/speaker is misrepresenting the opposition's argument by presenting a weaker argument than what the opposition truly has. Describe the stronger argument.

Reference: Cedarblom and Paulsen: 138

The following fallacies are category errors:

• Composition: because the parts have a property, the whole is said to have that property
• Division: because the whole has a property, the parts are said to have that property

These fallacies occur because the author mistakenly assumes that the whole is nothing more than the sum of its parts. However, things joined together may have different properties as a whole than any of them do separately.

1. Composition:

Because the parts of a whole have a certain property, it is argued that the whole has that property. That whole may be either an object composed of different parts or a collection/set of individual members.

Examples:

1. The brick wall is six feet tall. Thus, the bricks in the wall are six feet tall.
2. Germany is a militant country. Thus, each German is militant.
3. Conventional bombs did more damage in W.W. II than nuclear bombs. Thus, a conventional bomb is more dangerous than a nuclear bomb. (From Copi, p. 118)

Convincing Others: Show that the properties in question are the properties of the whole and not of each part or member or the whole. Perhaps describe the parts to show that they do not necessarily have the properties of the whole.

References: Barker: 164; Copi and Cohen: 117

2. Division:

Because the whole has a certain property, it is argued that the parts have that property. The whole in question may be either a whole object or a collection or set of individual members.

Examples:

1. Each brick is three inches high. Thus, the brick wall is three inches high.
2. Because the brain is capable of consciousness, each neural cell in the brain must be capable of consciousness.

Convincing Others: Show that the properties in question are the properties of the parts and not of the whole. Perhaps describe the parts to show that they do not necessarily have the properties of the whole.

References: Barker: 164; Copi and Cohen: 119

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