Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

A syllogism is defined as “a discourse in which, certain things having been posited and granted, something other than them necessarily follows because those things have been posited.” We should know that a syllogism aims to order reasoning according to the connection of terms with one another, not, as induction does, through resolution and reduction to singulars. It must therefore regard extremes capable of being united with one another, and a rationale or middle term on account of which they are united. Hence, from a middle term applied or united to the extremes, it unites them and infers that the extremes are united with one another. This is the whole order and progression of a syllogism: to infer and deduce a proposition in which two terms, or extremes, are united, from another proposition or propositions in which the middle term, or rationale by which they can and ought to be united with one another, is made explicit. That is why the definition says that it is “a discourse in which, certain things having been posited”—namely, the premises, in which the middle term is applied to the extremes—“something else necessarily follows,” that is, the conclusion is inferred, in which the extremes are joined to one another, “because those things have been posited,” that is, by the force and positing of the premises. An example is this syllogism: “Every body is a substance; every man is a body; therefore every man is a substance.” Here you see three propositions: two premises that infer, and a third that is the conclusion. In the third, the two extremes “man” and “substance” are united; in the premises, the middle term, on account of which those extremes are united, is applied to the extremes. The middle term is “body,” which, because it belongs to man and to substance, makes man and substance belong together.

A syllogism, then, consists of matter and form, like any artifact. Its FORM is the very arrangement and art that orders and disposes the matter so that it can properly infer and conclude. Its matter is twofold: one is proximate, the other remote. The proximate matter consists of the propositions from which the syllogism is constructed; the remote matter consists of the terms or extremes that compose the proposition and into which the syllogism is ultimately resolved. Therefore Aristotle defines a term in this part of logic as that into which a proposition is resolved, as into subject and predicate.¹ It is defined by resolution, as St. Thomas says in Opusculum 48, treatise on the Syllogism, chapter 1,² because our knowledge and judgment proceed by resolving a thing into its causes. Thus, insofar as a term serves the judging or resolving part, it is defined by resolution, not by composition. The definition says “as into predicate and subject” because the verb is not a term with respect to the syllogism, but a union; a term is only what functions as an extreme that infers or is inferred. Through the union expressed by the verb, then, there is composed not only what pertains to the truth of an enunciation, but also what pertains to the inferential connection. Thus the union, or copula, of the verb is not that into which the syllogism is resolved, but that which is dissolved when the syllogism is resolved.

Therefore, there are only three propositions in a syllogism: two premises, which infer, and one conclusion, which is inferred. The first premise is called the major proposition, the second the minor, and the third the conclusion or consequent. Similarly, there can be only three terms, although they are repeated in the three propositions. Two are the extremes, which are to be united in the conclusion; the other is the middle, which is united to the extremes in the premises but does not enter the conclusion, for it infers it. One extreme is called major, the other minor. The major extreme is the one taken in the major premise and placed in the conclusion. The minor extreme is the one taken in the minor premise and placed in the conclusion. The middle is the term posited twice in the premises but not in the conclusion. By “term” we mean not only something simple or uncomplex, but also something complex, provided that it functions as one extreme or middle.

The FORM of a syllogism can also be said to be twofold, corresponding to this twofold proximate and remote matter. Since the form of a syllogism is the ordering or arrangement of its matter, the arrangement that orders the remote matter, namely, the terms, is called a figure; the arrangement that orders the proximate matter, namely, the propositions, is called a mode. A figure in a syllogism, then, is the arrangement of terms according to the subject and predicate positions. A mode is the ordering of premises or propositions according to their proper quantity and quality. The proper quality is that at least one premise be affirmative, and that not all be negative. The proper quantity is that at least one be universal, and that not all be particular. Figures are determined according to the predication and subjection of the middle term with respect to the extremes; different figures result from different combinations of predication and subjection, as we shall say in the next chapter.