Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

In the past, it was considered very difficult to understand perfectly and clearly the discovery of a middle term. Now this matter is readily explained—not, as some think, by merely assigning as the middle term that which is the cause and rationale for the predicate belonging to the subject, or, as others put it, by taking as the middle term in order to conclude an affirmative conclusion that with which the things are identified, and in order to conclude a negative one that with which one extreme is identified and from which the other is separated. For what we are asking is precisely what that is in which the extremes are identified or one of them is separated, and what is the rationale and cause for the predicate belonging to the subject. One may consult the brief work of St. Thomas on this, the fiftieth among his opuscula.¹

We should therefore observe that every conclusion to be inferred is either a universal affirmative, a universal negative, a particular affirmative, or a particular negative. Since the term taken as the middle must be communicated and united to the extremes, or separated from one of them, so that the extremes themselves may be united or separated—and since the extremes capable of being united with one another are the subject and predicate in the conclusion—we must take as a middle term that unites or divides them either something that is a higher or lower predicate, something equal, or something incompatible or extraneous. The ancients called a higher or equal predicate a consequent term, because it follows from another: for example, from “man” one infers “animal,” which is higher, and “capable of laughter,” which is equal, since both are contained in man. They called a lower predicate an antecedent term, because it entails but is not entailed by what is higher: “man” does not follow from “animal,” but the reverse does. They called an incompatible predicate an extraneous term.

Therefore, to infer a universal affirmative, which is concluded only in Barbara, we take as middle term something consequent upon the subject, whether the predicate is higher or equal, and antecedent to the predicate, that is, something lower than it. For example, if you want to prove that every man is an animal, take “capable of laughter” as the middle term: it follows from “man” and entails “animal,” or is antecedent to “animal.” Thus: “Everything capable of laughter is an animal; every man is capable of laughter; therefore every man is an animal.”

To infer a universal negative, take as middle term what follows from the subject and is incompatible with the predicate. This is done in Celarent, the second mode of the first figure, and in Cesare, the first mode of the second. In Camestres, however, where the minor premise is negative, the middle must be sought in the reverse way: something incompatible with the subject and consequent upon the predicate, since it must be removed from the minor extreme and follow from the major. For example, to conclude that no man is a stone, “rational” or “capable of laughter” is a good middle term in Celarent and Cesare, since it follows from man and is incompatible with stone; in Camestres, the middle is “insentient,” which belongs to stone and is incompatible with man.

To infer a particular affirmative in the first figure, as in Darii, a suitable middle term is one that follows from the subject and is antecedent to the predicate. Thus, to infer that some animal is a substance, a suitable middle term is “sensible,” which follows from animal and entails substance. If the conclusion is inferred in the third figure (for a particular affirmative is not inferred in the second), as in Darapti or Disamis, the suitable middle term is one that is antecedent—that is, lower than both the predicate and subject—and that must be made subject in both premises. For example, “man” serves to infer that some animal is a substance, because man is an animal and is a substance.

Finally, to infer a particular negative, which can be concluded in all three figures, if it is inferred in the first figure, take as middle term something that follows from the subject and is incompatible with the predicate. For example, to conclude that some animal is not a stone, I take “man” as the middle term, saying: “No man is a stone; some animal is a man.” Or, if I want to conclude “Some animal is not a horse,” I take “rational,” which follows from some animal and is incompatible with horse, and say: “Nothing rational is a horse; some animal is rational,” etc. If a particular negative is inferred in the second figure, in the third mode, Festino, the same middle term is taken as in the first figure. In Baroco, however, the middle term taken is something extraneous to the subject and consequent upon the predicate. Thus, in the conclusion given above, “Some animal is not a stone,” we take “insentient” as the middle term, which is incompatible with animal and follows from stone. Finally, if the conclusion is inferred in the third figure, take as middle term something antecedent—that is, lower than the subject—and extraneous or incompatible with the predicate; for the conclusion given above, take “rational,” which is lower than animal and incompatible with stone.