Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

The division of syllogism can be taken either from the side of matter or from the side of form. First, on the side of matter, there is the division belonging to the books of the Posterior Analytics: a syllogism is fourfold—demonstrative, probable, sophistical, or erroneous. A demonstrative syllogism generates knowledge and consists of necessary matter; a probable syllogism consists of contingent matter and generates opinion; an erroneous syllogism consists of remote matter and generates error; a sophistical syllogism does not observe correct rules but fallacious ones, and generates deception.

Second, a syllogism is divided into common and expositional. A common syllogism is one in which a common term is posited as the middle; an expositional syllogism is one in which a singular term is posited as the middle. This division, then, is taken from the side of matter, since it is based on the terms.

It can also be divided into hypothetical and categorical, and into affirmative and negative, according to the propositions of which it consists.

On the side of form, a syllogism is first divided by the three figures. In each figure there are several modes, namely sixteen, both useful and useless, perfect and imperfect; but all are reduced to nineteen useful modes, which are contained in these verses:

First: Barbara, Celarent, Darii, Ferio, Baralipton. Celantes, Dabitis, Fapesmo, Frisesomorum. Second: Cesare, Camestres, Festino, Baroco. Third: Darapti, Felapton, Disamis, Datisi, Bocardo, Ferison.

A perfect mode is one in which the regulative principles of syllogisms are perfectly preserved; these are “Dici de omni” and “Dici de nullo,” as will be explained below. An imperfect mode is one in which these principles are not perfectly preserved, and which can therefore be reduced to a perfect mode. A useful mode is one in which the rules necessary for a good consequence are preserved; a useless mode is one in which those rules are not preserved. A direct mode concludes directly by predicating the major extreme of the minor in the conclusion; an indirect mode concludes conversely, by predicating the minor extreme of the major extreme in the conclusion.

THAT THERE ARE THREE FIGURES, and no more, is clear, because there can be only four combinations: either the middle is predicated in both premises, or is subject in both, or is subject in the major and predicate in the minor, or finally is predicate in the major and subject in the minor. It must nevertheless be observed that this last of the four combinations concludes indirectly. Since syllogisms that conclude indirectly are reduced to direct ones, the fourth figure, which always concludes indirectly, is therefore always reduced to the first by transposing the premises; it is consequently not counted separately, as though it were not distinct from the first. A syllogism is said to conclude directly when the major extreme is predicated in the conclusion of the minor extreme; it concludes indirectly when the reverse occurs, because the major extreme is the higher extreme, and it belongs to the higher to be predicated directly, while it belongs to the lower to be made subject. Thus, for it to be predicated in the conclusion of the minor extreme, it must also be predicated in the major premise of the middle as something higher. Therefore the direct figure is one in which the middle is subject in the major premise and the major extreme is predicated of it: this is the first figure. If, however, the middle is predicated in the major premise and the major extreme is made subject, the conclusion will be indirect; the syllogism must therefore be reduced to the first figure by transposing the premises. Accordingly, the fourth figure is not admitted as distinct but is reduced to the first, because figures are divided only by a different, natural, and direct way of concluding, not by an indirect one, since the latter belongs to and is reduced to the direct way.

Thus there remain three distinct figures: the first, in which the middle is subject in the major premise and predicate in the minor; the second, in which the middle is predicate in both premises; and the third, in which the middle is subject in both. We shall give examples below, enumerating all the modes of the figures.