Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

Some think that no syllogism needs to be reduced to another, more perfect syllogism; instead, all are regulated just as immediately by the principle: “Whatever things are identical to one third are identical to one another.” Thus, they can be shown immediately by this principle, and not by reduction to another syllogism, because just as in the first four modes of the first figure the extremes are identified with one third, so too in the other syllogisms of the second and third figures, as is clear from any syllogism made in those figures. Therefore, by such a principle one can immediately convince anyone who denies the inference of such syllogisms, and reduction to the first syllogisms of the first figure is not necessary.

Moreover, the Philosopher expressly teaches that all imperfect syllogisms can be reduced to universal syllogisms of the first figure, as is clear in 1 Prior., chapter 7.¹ St. Thomas teaches the same in opusculum 48, On the Syllogism, chapters 6, 7,² and 8.³ And the reason is that although the whole force of syllogism consists in the principle that whatever things are identified with one third are identified with one another, nevertheless, for this identification with one third to be clear, that third must be distributed. For if the middle is held particularly in both premises, nothing follows from pure particulars. If, then, the middle must be identified with the extremes according to distribution, by which it contains and unites the extremes themselves within it, this identification of the middle must be regulated by the principles “Dici de omni” and “Dici de nullo.”

This does not occur with equal evidence in all syllogisms, because it is not equally immediate and self-evident in all that some extreme is contained under the distributed middle itself, as is clear in the first four modes of the first figure. In these, the middle is subject in the major premise and predicate in the minor; consequently, since it is posited universally in the major on the side of the subject, it is then predicated of something in the minor. Hence, precisely by this fact, that of which it is predicated is shown to be contained under the middle itself. This is not made equally clear in the second and third figures, as is evident if we form a syllogism in Barbara: “Every animal is a substance; every man is an animal; therefore every man is a substance.” There the middle term “animal,” in which man and substance are identified, is posited universally on the side of the subject in the major premise. Then, in the minor, since animal is predicated of man, it is clear by this very fact that man is contained under animal, and consequently that substance, which was predicated of animal, will also be predicated by the rule “Dici de omni” of man, who is contained under animal.

This, however, is not made self-evident in the second and third figures. Therefore, for it to be clear that the extremes are thus identified with one third in such a way that “Dici de omni” or “Dici de nullo” is preserved in it, the syllogism must be reduced to the mode of the first figure, and not merely proved immediately by the principle “Whatever things are identical to one third, etc.,” excluding the principles “Dici de omni” and “Dici de nullo.”

As to whether the fourth figure exists, some dispute at greater length. For this difficulty, however, what we taught in the Summulae, book 3, chapter 5, is sufficient. We do not deny this fourth figure; rather, we say that it is reduced to the first and therefore does not constitute a wholly distinct figure, but is contained under the first.