This method of reduction is called Reductio ad impossibile, or Reductio per impossibile,[341] or Deductio ad impossibile, or Deductio ad absurdum. It is the only way of reducing AOO in figure 2 or OAO in figure 3 to figure 1, unless negative terms are used (as in obversion and contraposition); and it was adopted by the old writers in consequence of their objection to negative terms.
[341] Compare Mansel’s Aldrich, pp. 88, 89.
It will be shewn [later on] in this chapter that by employing the method of indirect reduction systematically we can bring out with great clearness the relation between the different moods and figures of the syllogism.
258. The mnemonic lines Barbara, Celarent, &c.—The mnemonic hexameter verses (which are spoken of by De Morgan as “the magic words by which the different moods have been denoted for many centuries, words which I take to be more full of meaning than any that ever were made”) are usually given as follows: 320
Barbără, Cēlārent, Dărĭi, Fĕrĭōque prioris:
Cēsărĕ, Cāmēstres, Festīnŏ, Bărōcŏ, secundae:
Tertia, Dāraptī, Dĭsămis, Dātīsĭ, Fĕlapton,
Bōcardō, Fērīsŏn, habet: Quarta insuper addit
Brāmantip, Cămĕnes, Dĭmăris, Fēsāpŏ, Frĕsīson.
Each valid mood in every figure, unless it be a subaltern mood, is here represented by a separate word; and in the case of a mood in any of the so-called imperfect figures (i.e., figures 2, 3, 4), the mnemonic gives full information for its reduction to figure 1, the so-called perfect figure.
The only meaningless letters are b (not initial), d (not initial), l, n, r, t ; the signification of the remainder is as follows:—
The vowels give the quality and quantity of the propositions of which the syllogism is composed; and, therefore, really give the syllogism itself, if the figure is also known. Thus, Camenes in figure 4 represents the syllogism—
| All P is M, | |
| No M is S, | |
| therefore, | No S is P. |
The initial letters in the case of figures 2, 3, 4 shew to which of the moods of figure 1 the given mood is to be reduced, namely, to that which has the same initial letter. The letters B, C, D, F were chosen for the moods of figure 1 as being the first four consonants in the alphabet.