n one of the premises, and unless both the premises are granted,
strictly syllogistic reasoning does not get under way.

Nevertheless, the syllogism has great practical value for the reasoning
and arguments of everyday life: in the first place it affords a means of
expanding and scrutinizing the condensed forms of reasoning which are so
common and so useful; and in the second place it can be used to sum up
and state the results of a course of reasoning in incontrovertible form.
I shall examine and illustrate both these uses of the syllogism; but
first I shall give certain rules which govern all sound reasoning
through syllogisms. They were invented by Aristotle, the great Greek
philosopher.

42. The Rules of the Syllogism. (A term is said to be distributed,
or taken universally, when the proposition of which it is a part makes a
statement about all the objects included in the term. In the proposition
_All men are mortal_, the term _men_ is obviously distributed, but
_mortals_ is not; for no assertion is made about all mortals but only
about those that are included under all men. In the proposition _No hens
are intelligent_, both terms are distributed; for the assertion covers
all hens, and also the whole class of intelligent beings, since it is
asserted of the class as a whole that it contains no hens.)

I. A syllogism must contain three terms, and not more than three
terms.

This rule is to be understood as guarding against ambiguity, especially
in the middle term; if the middle term, or either of the others, can be
understood in two ways, the syllogism will not hold water.

II. A syllogism must consist of three and only three propositions.
The reasons for this rule are sufficiently obvious.

III. The middle term of the syllogism must be distributed at least once
in the premises.

If it were not thus distributed or taken universally, the two premises
might refer to separate parts of the middle term, and so there would be
no meeting ground on which to form the conclusion. In the syllogism,
All good athletes lend a clean life, These men lead a clean life,
Therefore these men are good athletes, the fallacy lies in the fact
that in neither premise is any assertion made about all men who lead a
clean life. This fallacy, which is not uncommon in practice where the
terms are complicated, is known as the fallacy of the undistributed
middle.

IV. No term must be distributed in the conclusion unless it was
distributed