A complete syllogism has just been given: The man is a patriot; a patriot is a valuable citizen; hence the man is a valuable citizen.
It is possible to draw a third proposition only from two that have one term in common. It follows that there are three terms in a syllogism,—the first and second propositions having one term alike, and each having a particular term which reappears in the third proposition. This third proposition is that which the endeavor is made to prove. To establish a proposition by syllogism, then, it is necessary to find two others which contain each one of its terms, and which have a term in common. It is necessary to add that not from every pair of propositions which contain a common term is it possible to draw a third, and thus to form a syllogism. If we say, “A rose is a flower,” “A lily is a flower,” we have two propositions which have a common term, yet we cannot go on to make the third proposition, “Hence a rose is a lily.” The term which is common to both propositions must in one of them be spoken of as a whole, or in a general way. Logicians say that it must be “distributed;” in other words, one assertion must cover the term in its entire extent. In the first syllogism which we examined, the common—it is usually called the “middle”—term is in the second proposition spoken of in a general way. “A patriot is a valuable citizen” is an assertion of all patriots. In the false syllogism, “A rose is a flower; a lily is a flower,” there is nothing said of all flowers, and yet “flower” is the middle term. The rose is one flower, the lily is one flower, but until there is something said of all flowers it is not possible to draw out a new conclusion,—to form a syllogism.
He who wishes to exercise his wits with pretty mental gymnastics may learn from books on logic that there are a great many varieties of syllogisms. There are twenty-four valid ones, and a crowd of poor relatives, which exist under the discrediting title, “imperfect syllogisms,” and which, paradoxically, are of no use until they have been “reduced.” When it is added that each has a fine Latin name, the reader may appreciate that he is here being spared a good deal.
Although it is not possible to take space for a very intricate example of the skeleton of an argument, it is hardly fair to give nothing more complex than a simple syllogism; and the following may assist the formation of a more clear conception of the form in which reasoning should be put. Suppose the proposition which is to be proved to be, “The Norsemen discovered America before Columbus.”
Taking a few of the more obvious arguments which might be advanced in support of this proposition, and arranging them so as to begin with the more generally allowed and easily proved, we have:
1. The frequent appearance in European literature before Columbus of allusions to a land across the sea.
2. The story in the Icelandic Sagas.
3. Norse remains in America.
These proofs will be sufficient for purposes of illustration. Let us examine them in detail a little. Under each of these proofs—which it is convenient to call subordinate propositions—lies a syllogism, whether it is fully stated or not. The writer must be entirely clear in his own mind what this is, whether it seem to him well to state it explicitly or not. Here the syllogism of the first subordinate proposition, briefly stated, is:—
Allusions to a land over sea prove knowledge of such a land.