The student will observe that each statement in the syllogism is composed of two terms and that each term appears twice in the entire syllogism, but only once in any one statement. The major term represents the largest element in the syllogism namely,—the class of persons who should study argumentation. The minor term represents the smallest element in the syllogism namely,—Paul Morton, the particular person about whom a conclusion is reached. The middle term serves as an intermediary or connecting link which binds the minor term to the major term. It does not appear in the conclusion but is cast away after it has served its purpose in assigning the minor term,—Paul Morton, to the major term,—those who should study argumentation.
In the typical form of the syllogism with which we are concerned the major premise should always be in the universal affirmative-form. By universal affirmative is meant that the assertion is made with regard to the class as a whole as: “All men are mortal,” “All laws should be obeyed,” “All students should pay their bills,” etc. No part of the class of persons, events, or things about which an assertion is made should be left outside the statement as would be the case if the statements read—“Some laws should be obeyed,” “Some students should pay their bills.”
From the foregoing discussion it is evident that the deductive syllogism, in order to be valid, must be constructed in accordance with certain well defined rules. In books of logic the student will find these rules discussed at some length and their application set forth in detail. For our purpose it is only necessary to refer to them and keep them clearly in mind in connection with the discussion here given. The rules of the syllogism with which we are concerned are as follows:
1. A syllogism must contain three terms, Major term, Minor term, and Middle term.
2. A syllogism must consist of three complete statements, Major Premise, Minor Premise, and Conclusion.
3. The middle term must be distributed at least once in the premises. A term is distributed when it is universal in its application or taken in its whole length of meaning.
4. A term cannot be distributed in the conclusion unless it is distributed in the premises.
5. No conclusion can be drawn from two negative premises.
6. A negative conclusion always follows one negative premise and a negative conclusion cannot be obtained unless one of the premises is negative.
For the purpose of making more plain the relation between the terms and the statements in a syllogism let us consider the old method of graphical representation by means of circles.