The Making of Arguments

by J. H. Gardiner

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.

V. No conclusion can be drawn from two negative premises.

In other words, if both the major term and the minor term lie outside the middle term, the syllogism gives us no means of knowing what their relation is to each other. The following example will make the reason clear: No amateur athlete has a salary for playing, John Gorman is not an amateur athlete, Therefore John Gorman has a salary for playing.

VI. If one of the premises is negative, the conclusion must be negative.

If of the major and minor premise one is negative, then either the major or the minor term does not agree with the middle term, and the other does; therefore the major and minor term cannot agree with each other.

43. The Syllogism in Practical Use. The practical value of the syllogism and its rules comes in the first place, as I have said, when we expand a condensed form of reasoning into its full grounds in the form of a syllogism. Our reasoned judgments ordinarily take the shortened form, Socrates is mortal, because he is a man; The Corporation Tax Bill is constitutional, because it is a tax on a way of doing business. In each of these cases we are reasoning from a general principle, which is previously established, and from a particular way of conceiving the special fact before us, but we assume the general principle as understood. In the cases above the meaning is clear without declaring at length, All men are mortal, or All taxes on a way of doing business are constitutional.

At any time, however, when you find a piece of reasoning in this condensed form, whether your own or some one else's, which seems to you suspicious, if you expand it into a full syllogism you will have all its parts laid bare for scrutiny. Take, for example, the assertion, "Robinson Crusoe" must be a true story, for everything in it is so minutely described: if you expand it into the full syllogism, All books in which the description is minute are true, "Robinson Crusoe" is a book in which the description is minute, Therefore "Robinson Crusoe" is true, you would at once stick at the major premise. So where you suspect an ambiguity in the use of terms, you can bring it to the surface, if it is there, by the same sort of expansion. In the argument, Bachelors should be punished, because they break a law of nature, the ambiguity becomes obvious when you expand: All law breakers should be punished, Bachelors break a law of nature, Therefore bachelors should be punished; at once you see that law is used in two senses, one the law of the land, the other the statement of a uniformity in nature. In the argument, These men are good citizens, for they take an interest in politics, the expansion to All good citizens are interested in politics, These men are interested in politics, Therefore these men are good citizens,[⁴¹][!--Note--] shows that the reasoning contains a breach of the third rule of the syllogism (see p. 148) and is therefore a case of the fallacy of the undistributed middle.

Whenever you make or find an assertion with a reason attached by such a word as "since," "for," or "because," or an assertion with a consequence attached by a word like "therefore," "hence," or "accordingly," you have a case of this condensed reasoning, which, theoretically at any rate, you can expand into a full syllogism, and so go over the reasoning link by link.