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 in at least one of the premises.

In other words, if you have premises which deal with part of a class only, you cannot reach a conclusion about the whole class.  In the syllogism, All newspaper editors know how to write, All newspaper editors are paid, Therefore all men who know how to write are paid, the fallacy is obvious.  But in the following, All bitter partisans are dangerous citizens, This man is not a bitter partisan, Therefore this man is not a dangerous citizen, one may have to scrutinize the reasoning a little to see that the fallacy lies in the fact that dangerous citizen is taken universally in the conclusion, since a proposition with a negative predicate makes an assertion about the whole of its predicate, but that it is not taken universally in the premise in which it occurs.  A fallacy which thus arises from not noticing that a negative predicate distributes its term is apt to be insidious.