Figures and Moods of the Syllogism
The four Figures of the syllogism (determined by the position of the middle term), the special laws governing each Figure, and the valid Moods — the 19 combinations of A, E, I, O propositions that survive the laws of syllogism.
The Figure of a syllogism is determined by the position of the middle term: First Figure (subject of major, predicate of minor), Second Figure (predicate of both), Third Figure (subject of both), Fourth Figure (predicate of major, subject of minor). Each Figure has special laws derived from the general ones. The Mood is determined by the types (A, E, I, O) of the three propositions in order (major, minor, conclusion). The 19 valid moods identified by their mnemonic names are: First — Barbara, Celarent, Darii, Ferio; Second — Cesare, Camestres, Festino, Baroco; Third — Darapti, Disamis, Datisi, Felapton, Bocardo, Ferison; Fourth — Bramantip, Camenes, Dimaris, Fesapo, Fresison. The vowels in each mnemonic name encode the mood; the consonants encode the reduction instructions.
a) Figures of the Syllogism
The position of the middle term in the premisses determines the Figure of the syllogism. The middle term can occupy four positions:
| Figure | Position of Middle Term |
|---|---|
| First | Subject of major premiss, predicate of minor |
| Second | Predicate of both premisses |
| Third | Subject of both premisses |
| Fourth | Predicate of major premiss, subject of minor |
Taking S for the minor term (subject of conclusion), P for the major term (predicate of conclusion), and M for the middle term:
Fig. I Fig. II Fig. III Fig. IV
M — P P — M M — P P — M
S — M S — M M — S M — S
S — P S — P S — P S — PA mnemonic: these patterns resemble the four strokes of the letter M.
The First Figure is the most perfect, showing most clearly the logical consequence of the argument. The Second and Third have value. The Fourth is negligible, being an inversion of the First.
Special Laws of the Three Valuable Figures
(Derived from the Eight General Laws of the Categorical Syllogism)
| Figure | Special Laws |
|---|---|
| Figure I | Major premiss must be universal; minor premiss must be affirmative. |
| Figure II | Major premiss must be universal; one premiss must be negative. |
| Figure III | Minor premiss must be affirmative; conclusion will be particular. |
b) Moods of the Syllogism
The mood of a syllogism is the state resulting from the arrangement of its propositions with respect to their quantity and quality. A syllogism with three A-propositions is in mood AAA; one with E, A, E propositions is EAE; and so on.
There are mathematically 64 possible arrangements of three propositions chosen from four types (A, E, I, O). Applying the eight general laws of the syllogism, 53 of these are invalid (involving negative premisses without negative conclusion, universal conclusion without warrant, particular premisses, etc.). The eleven valid moods remaining are:
AAA, AAI, AEE, All, AOO, EAE, EAO, EIO, IAI, OAO.
(AEO may be omitted as it is contained in AEE, since O is the subalternate of E.)
Not all eleven moods are valid in all four figures; the special laws of figures eliminate further combinations. The result is 19 valid moods distributed as follows:
| Figure | Valid Moods |
|---|---|
| First | AAA, EAE, AII, EIO |
| Second | EAE, AEE, EIO, AOO |
| Third | AAI, IAI, AII, EAO, OAO, EIO |
| Fourth | AAI, AEE, IAI, EAO, EIO |
Reduction of Syllogisms
The First Figure is most perfect; therefore Dialecticians have formulated a system for reducing syllogisms of the Second, Third, and Fourth Figures to the First Figure — restating them in First Figure shape to clarify their logical consequence.
The method of reduction is set out fully in the Appendix. In summary: the valid moods of all four figures are given traditional Latin names whose vowels indicate the proposition types, and whose consonants give instructions for the reduction:
- s — convert simply the premiss indicated by the preceding vowel
- p — convert per accidens (accidentally) the premiss indicated
- m — transpose the major and minor premisses
- c — reduction is indirect
The mnemonic names are:
Barbara, Celarent, Darii, Ferio (First Figure) Cesare, Camestres, Festino, Baroco (Second Figure) Darapti, Disamis, Datisi, Felapton, Bocardo, Ferison (Third Figure) Bramantip, Camenes, Dimaris, Fesapo, Fresison (Fourth Figure)
The practical value of reduction is mainly as mental training; as Lepidi observes, if the matter is found difficult for beginners, it may be omitted without great loss.
Summary of the Article
We have learned what is meant by the Figures and the Moods of the syllogism. We have studied the special laws — derived from the Eight General Laws — by which each Figure is regulated, and have seen these applied in examples. We have sifted the valid Moods from all possible arrangements of premisses, assigned to each Figure the Moods that may occur in it validly, and studied the meaning of reduction to the First Figure.