A Class Room Logic / Deductive and Inductive, with Special Application to the Science and Art of Teaching

by George Hastings McNair

(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.