It is natural for the syllogism to appear at first a somewhat cumbersome and artificial mode of expressing our everyday reasoning. We pointed out at the beginning, however, that to make sure of the correctness of arguments, it is necessary to be both full and explicit in statement, and the syllogism is merely a fully expanded form which we use when we undertake to prove one proposition by other propositions. It is true, none the less, that actual arguments do not always appear in this fully expanded form. In perhaps a majority of the instances, they appear with one of the three proposition omitted or suppressed. A deductive argument with one of its propositions thus missing is called an enthymeme (from a combination of Greek words signifying “in the mind”). As already intimated, the missing proposition may be the major premise, the minor premise, or the conclusion. In every instance the one to whom the argument is addressed is supposed to supply the missing proposition. Let us suppose that someone presents the argument “X would make an ideal candidate for president because he was born in a log cabin.” It is evident after a moment’s analysis that we have here the minor premise and the conclusion of a syllogism. The major premise, which is “All who were born in log cabins make ideal candidates for president,” has been withheld.“Every American is pledged to do his duty, and you are an American” is another form of the enthymeme. Here it is the conclusion “You are Pledged to do your duty” which is withheld. In the enthymeme “All property owners should vote for the bond issue; you should vote for the bond issue” it is the minor premise which must supplied.
Since a great many of the world’s arguments appear in the form of enthymemes, it is of great value to acquire some facility in expanding the enthymeme into a complete syllogism. Then, whether or not we shall be persuaded by the argument will depend upon whether or not we accept both of the premises. And even if we can accept both of the premises, we must be able to see whether the conclusion emerges in accordance with the formal rules of the syllogism.
The missing proposition of an enthymeme is sometimes suppressed because the maker of the argument knows that if we look carefully at his premises, we may question or reject one of them. He wishes to sneak his suppressed premise by unnoticed. It is not unfair to say that a large fraction of advertising is presented in the form of enthymemes for just this purpose, and the student of logic will find it a valuable exercise to go through the pages of any popular magazine and determine the suppressed premise in the texts of advertisements. The same may be said of a considerable part of political argumentation, and even of those arguments heard from supposedly non-partisan sources. It is a good rule always to stay on the alert to see on what the maker of an argument is really basing his case.
Still, all enthymemes are not offered with the object of deceiving or imposing upon the unwary. Many enthymemic arguments are perfectly frank and honest, the maker feeling that the unstated premise is too obvious or too generally accepted to require stating. It is ‘in the mind’ of everyone he is addressing.
For this very reason the enthymeme has been called since ancient times the rhetorical syllogism. This expression requires a little interpretation, but an understanding of it is essential to the remainder of what we have to say about argumentation.