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] 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.