6. MNEMONIC LINES.
As a device for remembering the 19 valid moods, the logicians of an earlier day originated a combination of coined words which, though rather unscientific, may be easily committed to memory. Since, however, it is of much more value to test the moods by means of the general rules of the syllogism than it is to try to remember these moods, the mnemonic lines are of slight value. They are treated here merely as an item of historical interest.
(1) Barbara, Celarent, Darii, Ferioque prioris;
(2) Cesare, Camestres, Festino, Baroko, secundæ;
(3) Tertia, Darapti, Disamis, Datisi, Felapton, Bokardo, Ferison, habet; Quarta insuper addit
(4) Bramantip, Camenes, Dimaris, Fesapo, Fresison.
The only letters in these lines which mean nothing are l, n, r, t and small b and d; all the others have a signification. For example, the vowels of the italicizedwords signify the various valid moods, as e. g., the first line indicates the moods AAA, EAE, AII, EIO. The Latin words, printed in ordinary type, are intended to make evident that the moods indicated by the artificial italicized words of the first line, belong to the first figure; that the moods of the next four words, belong to the second figure; while the third figure includes the next six, and the fourth figure the last five. It is now seen that Festino, for example, stands for that mood of the second figure which has an E for its major premise, an I for its minor premise, and an O for its conclusion.
The first figure was called by Aristotle the perfect figure, whereas the second and third were the imperfect figures. The fourth figure was given no place in the works of Aristotle; its discovery is credited to Galen, a celebrated teacher of medicine of the second century. According to Aristotle, the first figure is the most serviceable and the most convincing and, therefore, as a final test of their validity, the moods of the other figures should be changed to the first. This process in logic is termed Reduction. In this reduction of the imperfect figures to the perfect, the capital letters of the artificial words, together with s, p, m, and k, have a definite meaning. The capital letters indicate that certain moods of the imperfect figures can be reduced to the corresponding moods of the first figure; e. g., Festino (eio) of the second figure, Felapton (eao) of the third figure, and Fesapo (eao) of the fourth figure may all be reduced to Ferio (eio) of the first figure. This is known because Fis the initial letter of each word. s signifies that the proposition denoted by the preceding vowel is to be converted simply. To illustrate: s in Fesapo means that the major premise E of the mood E
A
O of the fourth figure must be converted simply in order to change the mood to Ferio of the first figure. p indicates that the proposition represented by the vowel which precedes p must be converted by limitation (per accidens). m (mutare) makes evident that the premises are to be interchanged, the major of the old becoming the minor of the new, and the minor of the old becoming the major of the new. k denotes that the mood, such as Baroko, must be reduced by a special process known as indirect reduction. These directions may now be followed as illustrative of the process of reduction.
(1) Given: A syllogism in Darapti A
A
I
A All M
true teachers are G
just,
A All M
true teachers are S
sympathetic,
I ∴ Some S
sympathetic persons are G
just.
The symbols indicate that the mood is A
A
I or is in Darapti and that this mood is used in the third figure.
Problem: To reduce A
A
I of the third figure to some mood of the first figure.
Process: D, being the initial letter of Darapti, suggests that its mood must be reduced to one indicated by a word of the first figure whose initial letter is D. This mood is in Darii, or is A
I
I.
The p in Darapti indicates that the proposition represented by the preceding vowel must be converted by limitation. This proposition is the minor premise; converting it by limitation gives: “Some sympathetic persons are true teachers.” As there are no other significant letters the reduction is complete and we have this:
A All M
true teachers are G
just,
I Some S
sympathetic persons are M
true teachers,
I ∴ Some S
sympathetic persons are G
just.
The symbolization indicates that the mood is A
I
I of the first figure, or is in Darii.
(2) Given: A syllogism in Camestres A
E
E
A All G
true teachers are M
just,
E No S
one who shows partiality is M
just,
E ∴ No S
one who shows partiality is a G
true teacher.
The symbols show that the mood is AEE of the second figure or in Camestres. Judging from the initial letter C, the mood in Camestres must be reduced to the mood in Celarent E
A
E.
The letter m between a and e indicates that the major and minor premises of the given syllogism must be interchanged. The letters following both e’s suggest that the minor premise and the conclusion of the syllogism must be converted simply.
This is the resulting syllogism:
E No M
just person shows G
partiality,
A All S
true teachers are M
just persons,
E ∴ No S
true teacher shows G
partiality.
Here, then, is the E
A
E of the first figure or the mood in Celarent.
According to the ancient theory, reduction is necessary as a matter of final and absolute proof that the conclusionfollows from the given premises. But, as this claim has been satisfactorily refuted by modern logicians, we need not give more space to the process. The meaning of k, as related to “indirect reduction,” is explained in most of the earlier works on logic. See Hyslop, page 193.