Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

Since figures, as was said, are nothing other than different combinations according to the predication and subjection of the middle term, while moods are combinations according to the quantity and quality of propositions, sixteen combinations of moods can be made in each figure with respect to quantity and quality. For the quantity of propositions can vary in four ways: both premises may be universal, both particular, the first universal and the second particular, or conversely the first particular and the second universal. I say similarly of quality: both premises may be affirmative, both negative, the first affirmative and the second negative, or conversely the first negative and the second affirmative.

Thus, given four combinations with respect to quality and four with respect to quantity, quantity and quality can be combined with one another in sixteen ways, because each mood or combination of quantity admits four modes of quality, and conversely. For example, if both premises are universal—which is the first combination with respect to quantity—four modes of quality are possible: both universals may be affirmative, both negative, the first affirmative and the second negative, or conversely. Exactly the same can be done with every other combination. Since there are four combinations of quantity and four of quality, and each of the four modes can be combined with the others, sixteen moods result in each figure according to the different quantities and qualities.

But not all moods are useful, that is, valid and legitimate inferences. To discern which are useful and which useless in each figure, we must consider the rules required for validity in these syllogisms. A mood that observes all of them is useful; one that does not is useless.

Some rules required for a good syllogism are therefore general to all figures, and some are proper to each.

There are four COMMON RULES. First: Nothing follows from purely particular or indefinite premises. Second: Nothing follows from purely negative premises. The reason for both conditions is drawn from the general principle on which the whole structure of syllogism rests, as will be explained below: “Whatever things are the same as one third thing are the same as one another”; that is, because the extremes are united in something, they are united with one another. Therefore they must be united in at least one premise, and so they must not both be divided or denied in both premises. Likewise, the third thing in which they are united must include the extremes and be distributed with respect to them; otherwise it will not be said of all or of none. Therefore at least one premise must have distribution and affirmation. The third rule is that no term may be distributed in the conclusion unless it is distributed in the premises; otherwise one would argue from an undistributed term to a distributed one. Fourth: The middle term must not enter the conclusion, as was said. Thus every syllogism that yields a negative conclusion is negative, and one that yields a particular conclusion is particular.

From these general rules, four further PARTICULAR RULES for the individual figures are inferred. First: In the first figure, in moods that conclude directly, the major premise cannot be particular and the minor cannot be negative. The reason is that if the major is particular, the middle term is not distributed, since the middle must be subject in the major and predicate in the affirmative minor. If the minor is negative, it yields a negative conclusion in which some term would be distributed although it was not distributed in the affirmative premise. For example: “Every man is an animal; no horse is a man; therefore no horse is an animal.” Here “animal” is distributed in the conclusion but not in the premises. In moods that conclude indirectly, however, the major can be particular, because the middle is not subject in them, and the minor can be negative, as in Fapesmo and Frisesomorum. The second rule, for the second figure, is: If both premises are affirmative, nothing is concluded. The reason is that the middle term is predicated in both premises in the second figure and is therefore not distributed if both are affirmative. The third rule, for the same figure, is: If the major premise is particular, nothing follows. For in that case some term would be distributed in the conclusion but not in the premises. For example: “Some animal is a man; no horse is a man; therefore no horse is an animal.” Here “animal” is distributed in the conclusion but not in the premises. The fourth rule, for the third figure, is: If the minor is negative, nothing is concluded. For then the major must be affirmative, and its predicate will not be distributed, whereas it will be distributed in the conclusion. For example: “Every man is an animal; no man is a horse; therefore no horse is an animal.” Here “animal” is distributed in the conclusion but not in the premises.

Once these rules are seen, you can easily reject all useless moods in each figure. In the first figure, out of sixteen combinations, all four particular combinations and all four purely negative ones must be rejected by the first two general rules. Next, all those with a particular major and those with a negative minor must be rejected. Thus only four moods remain, in which either both premises are affirmative and the major universal, or one premise is negative and the minor affirmative. These are Barbara, Celarent, Darii, and Ferio. The vowels in those words, as we said in the preceding book, chapter on Conversion,¹ signify: A, a universal affirmative; E, a universal negative; I, a particular affirmative; O, a particular negative.

Nevertheless, since, as we said, the first two particular rules for the first figure are required only for direct, not indirect, conclusions, other indirectly concluding moods can be admitted in the first figure in which either the major is particular or the minor negative, provided they conclude indirectly, so that the major extreme is not predicated of the minor in the conclusion but is made subject. There are five such moods, named by these five words: Baralipton, Celantes, Dabitis, Fapesmo, Frisesomorum. In all of them an indirect conclusion is preserved, namely, the minor extreme is predicated of the major; yet not all of them have a particular major or negative minor, though either may occur. An example of a syllogism concluding directly in the first figure is: “Every animal is living; every man is an animal; therefore every man is living.” An example of one concluding indirectly, in Celantes, is: “No stone is an animal; every animal is sensitive; therefore no stone is sensitive.”

Likewise, in the second figure twelve of the sixteen possible combinations are excluded. Eight are excluded by the first two general rules, namely, those with purely particular premises and those with purely negative premises. The second and third rules also exclude the combination in which both premises are affirmative, and the combination in which the major is particular. Each of these combinations can occur twice: both premises affirmative with the first particular and second universal, or conversely; and both premises particular with the first affirmative and second negative, or conversely. Thus only four useful moods remain: Cesare, Camestres, Festino, and Baroco. An example is Cesare: “No animal is a stone; every marble is a stone; therefore no marble is an animal.”

Finally, in the third figure ten combinations are excluded: eight by the general rules. By the fourth rule, if the minor is negative, nothing is concluded, whether the first premise is particular and the second universal or conversely; this excludes two more combinations. Thus six useful moods remain: Darapti, Felapton, Disamis, Datisi, Bocardo, and Ferison.

Thus all the useful moods are nineteen, contained in the verses cited above.²

Note that in this third figure the first two moods, Darapti and Felapton, have both premises universal but conclude particularly, not universally. If they concluded universally, they would argue from an undistributed term to a distributed one, contrary to the third rule, as is clear in this Darapti syllogism: “Every animal is sensible; every animal is a substance; therefore every substance is sensible.” Here “substance” is distributed in the conclusion but not in the premises.