Aristotelian Syllogism: An Essential and Derivative Moods

Abstract: Aristotle’s most famous contribution to logic is the syllogism, which he discusses primarily in the Prior Analytics. A syllogism is a three-step argument containing three different terms. A simple example is “All men are mortal; Socrates is a man; therefore, Socrates is mortal.” This three-step argument contains three assertions consisting of the three terms Socrates, man, and mortal. It is generally accepted that it is a mistake that Aristotle ignore the moods of the fourth figure in his syllogism. In this paper I shall argue the Aristotelian Syllogism consisting of the essential moods and their derivative moods is complete or self-contained, all the moods of the fourth figure can be derived from the essential moods. The analysis table provided in the paper will contribute to showing the procedure from the essential moods to the derivative ones, and showing the distinction between the Aristotelian and the traditional syllogism. Some of the moods described by Aristotle are absent because the conventional syllogism tightly distinguishes the major premise from the minor one in a syllogism and strictly limits the major word and small one in the premise or the conclusion. I think the Aristotelian Syllogism is more flexible and feature-rich than the traditional one. If a syllogism contains the negative nouns and the quantified predicates, the number and type of syllogism will be greatly expanded, and cannot be described by the Aristotelian syllogism, let alone the traditional one.