From Stephen's Guide (14)

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Syllogistic Fallacies

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The fallacies in this section are all cases of invalid categorical syllogisms. Readers not familiar with categorical syllogisms should consult Stephen's Guide to Categorical Syllogisms.

The following are syllogistic fallacies

1. Fallacy of the Four Terms
(quaternio terminorum)

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Definition:
A standard form categorical syllogism contains four terms.
Examples:
(i) All dogs are animals, and all cats are mammals, so all dogs are mammals.
The four terms are: dogs, animals, cats and mammals.
Note:In many cases, the fallacy of four terms is a special case of equivocation. While the same word is used, the word has different meanings, and hence the word is treated as two different terms. Consider the following example:
(ii) Only man is born free, and no women are men, therefore, no women are born free.


The four terms are: man (in the sense of 'humanity'), man (in the sense of 'male'), women and born free.
Proof:
Identify the four terms and where necessary state the meaning of each term.

2. Undistributed Middle

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Definition:
The middle term in the premises of a standard form categorical syllogism never refers to all of the members of the category it describes.
Examples:
(i) All Russians were revolutionists, and all anarchists were revolutionist, therefore, all anarchists were Russians.
The middle term is 'revolutionist'. While both Russians and anarchists share the common property of being revolutionist, they may be separate groups of revolutionists, and so we cannot conclude that anarchists are otherwise the same as Russians in any way. Example from Copi and Cohen, 208.

(ii) All trespassers are shot, and someone was shot, therefore, someone was a trespasser.
The middle term is 'shot'. While 'someone' and 'trespassers' may share the property of being shot, it doesn't follow that the someone in question was a trespasser; he may have been the victim of a mugging.
Proof:
Show how each of the two categories identified in the conclusion could be separate groups even though they share a common property

3. Illicit Major

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Definition:
The predicate term of the conclusion refers to all members of that category, but the same term in the premises refers only to some members of that category.
Examples:
(i) All Texans are Americans, and no Californians are Texans, therefore, no Californians are Americans.
The predicate term in the conclusion is 'Americans'. The conclusion refers to all Americans (every American is not a Californian, according to the conclusion). But the premises refer only to some Americans (those that are Texans).
Proof:
Show that there may be other members of the predicate category not mentioned in the premises which are contrary to the conclusion.
For example, from (i) above, one might argue, "While it's true that all Texans are Americans, it is also true that Ronald Regan is American, but Ronald Regan is Californian, so it is not true that No Californians are Americans."

4. Fallacy of Drawing an Affirmative Conclusion From a Negative Premise

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Definition:
The conclusion of a standard form categorical syllogism is affirmative, but at least one of the premises is negative.
Examples:
(i) All mice are animals, and some animals are not dangerous, therefore some mice are dangerous.
(ii) No honest people steal, and all honest people pay taxes, so some people who steal pay pay taxes.

Proof:
Assume that the premises are true. Find an example which allows the premises to be true but which clearly contradicts the conclusion

5. Illicit Major

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Definition:
The predicate term of the conclusion refers to all members of that category, but the same term in the premises refers only to some members of that category.
Examples:
(i) All Texans are Americans, and no Californians are Texans, therefore, no Californians are Americans.
The predicate term in the conclusion is 'Americans'. The conclusion refers to all Americans (every American is not a Californian, according to the conclusion). But the premises refer only to some Americans (those that are Texans).
Proof:
Show that there may be other members of the predicate category not mentioned in the premises which are contrary to the conclusion.
For example, from (i) above, one might argue, "While it's true that all Texans are Americans, it is also true that Ronald Regan is American, but Ronald Regan is Californian, so it is not true that No Californians are Americans."

6. Fallacy of Exclusion

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Definition:
Important evidence which would undermine an inductive
argument is excluded from consideration. The requirement
that all relevant information be included is called the
"principle of total evidence".

Examples:
(i) Jones is Albertan, and most Albertans vote Tory, so Jones
will probably vote Tory. (The information left out is that
Jones lives in Edmonton, and that most people in Edmonton
vote Liberal or N.D.P.)
(ii) The Leafs will probably win this game because they've
won nine out of their last ten. (Eight of the Leafs' wins came
over last place teams, and today they are playing the first
place team.)

Proof:
Give the missing evidence and show that it changes the
outcome of the inductive argument. Note that it is not
sufficient simply to show that not all of the evidence was
included; it must be shown that the missing evidence will
change the conclusion.

7. Existential Fallacy

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Definition:
A standard form categorical syllogism with two universalpremises has a particular conclusion.
The idea is thatsome universal properties need not be instantiated. Itmay be true that 'all trespassers will be shot' even ifthere are no trespassers. It may be true that 'all brakelesstrains are dangerous' even though there are no brakelesstrains. That is the point of this fallacy.

Examples:
(i) All mice are animals, and all animals are dangerous, so some mice are dangerous.
(ii) No honest people steal, and all honest people pay taxes, so some homest people pay taxes.

Proof:
Assume that the premises are true, but that there are no instances of the category described. For example, in (i) above, assume there are no mice, and in (ii) above, assume there are no honest people. This shows that the conclusion is false