Rules of Validity
-  The Middle Term  -

1. The Middle Term Must Be Distributed at Least Once

This rule says that at least one of the premises in a syllogism must make a statement about the entire class designated by the middle term. Otherwise, the middle term will not provide a strong enough link between the other two terms to make the syllogism valid.

Example:
Consider the following:

All conservatives believe in private property.
All people who defend capitalism believe in private property.

Therefore, all people who defend capitalism are conservatives.

In each premise, the middle term is the predicate of an affirmative proposition. The middle term is therefore undistributed in both premises, and the argument violates the rule.

The fact that conservatives believe in private property does not mean that they are the only people who do. So the fact that pro- capitalists believe in private property does not necessarily mean that they are conservatives. They may or may not be.

The premises locate the two classes, P (conservatives) and S (pro-capitalists), within the wider class (M) of believers in private property. But that doesn't tell us whether S is included in P, or P in S, or whether there is any overlap at all. Again, there may or may not be.

S is distributed in the conclusion, but not in the minor premise. It is not valid to assume that what is true of all vertebrates (that they reproduce sexually) must be true of other species of the same genus. The only conclusion we can draw here is that some animals reproduce sexually. That is, we must keep S undistributed in the conclusion.


Comprehension

1 What is distributed in all universal categorical propositions?
a) only the subject
b) only the predicate
c) both the subject and the predicate
d) neither the subject or the predicate
2 What is distributed in all negative categorical propositions?
a) only the subject
b) only the predicate
c) both the subject and the predicate
d) neither the subject or the predicate
3 Which term is the middle term in a categorical syllogism?
a) the term that is the subject of the conclusion
b) the term that is the predicate of the conclusion
c) the term that is in both the major and the minor premises and that serves to link the two premises
4 Is the middle term of the following categorical syllogism distributed at least once?

All of Shakespeare's dramas are in blank verse
Some great plays are in blank verse


Some great plays are dramas of Shakespeare
a) yes
b) no
5 Is the middle term of the following categorical syllogism distributed at least once?

Some crimes against property are fraud
All frauds are felonies


Some felonies are crimes against property
a) yes
b) no
6 Is the middle term of the following categorical syllogism distributed at least once?

No horned animal is a predator
All moose are horned animals


No moose is a predator
a) yes
b) no
7 Is the middle term of the following categorical syllogism distributed at least once?

All P are M
Some M are S


Some S are P
a) yes
b) no
8 Is the middle term of the following categorical syllogism distributed at least once?

Some M is P
Some S is M


Some S is P
a) yes
b) no
9 Is the middle term of the following categorical syllogism distributed at least once?

Some M are not P
All S are M


Some S are not P
a) yes
b) no

The Middle Term | Distributed Terms |
Two Negative Premises | Negative Premises and Conclusions

Rules of Validity

© Copyright 1998, W.W. Norton & Co.