Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

An expository syllogism is said to be one “which has a singular term for its middle.” It is called expository, as St Thomas says in Opusc. 47,¹ because it is a kind of sensible resolution that, as it were, exposes the thing to the senses, as when you say: “Peter is white, Peter is running, therefore what is running is white.” And for this reason nearly all expository syllogisms are made in the third figure, because in it the middle is the subject in both premises, and a singular term is more suitably made subject than predicate. Yet it can also be made in the other figures. Since, however, the other extremes are common terms and not singular, all the conditions observed in other syllogisms must be observed in them, and the defects that may be found must be avoided. But since the middle itself is not a common term but a singular one, it can neither be distributed nor universalized; rather, it must be perfectly singularized. Hence, if it has not been perfectly and completely singularized, the syllogism will be defective. This must be observed especially with divine terms, in which the term “God,” “divine essence,” and others pertaining to the absolutes are singular in such a way that they are equivalently common, because in reality they are communicated to several persons. Hence they are not suited to an expository syllogism, as this is invalid: “This God is the Father, this God is the Son, therefore the Son is the Father,” because the middle is not perfectly singularized. Therefore one must use it as a common term and, consequently, if it is posited as the middle, it must be perfectly distributed, by saying: “Everything that is God is the Father; everything that is God is the Son,” etc.; but the premises are false.

Second, it is required that the middle, which is a singular term, be taken for the same individual; otherwise there is an equivocation of the middle, or a different sense, or the argument proceeds with four terms. Thus this is invalid: “This animal is a horse” (pointing to a horse), “this animal is a human being” (pointing to Peter), “therefore a human being is a horse,” because the middle is not taken for the same thing.

Third, when expository syllogisms are made in the third figure, care must be taken that the minor premise not be negative, in accordance with the rules of the third figure. For this reason the following is invalid: “Peter is a human being, Peter is not Paul, therefore Paul is not a human being.” Conversely, this is valid: “Peter is not Paul, Peter is a human being, therefore some human being is not Paul,” and it is in Ferison.