Ueberweg gives Camestros and Calemos for the weakened moods of Camestres and Calemes. This is not, however, quite accurate. The mnemonics should be Camestrop and Calemop.
Professor Carveth Read (Logic, pp. 126, 7) suggests an ingenious modification of the verses, so as to make each mnemonic immediately suggest the figure to which the corresponding mood belongs, at the same time abolishing all the unmeaning letters. He takes l as the sign of the first figure, n of the second, r of the third, and t of the fourth. The lines (to be scanned, says Professor Read, discreetly) then run
Ballala, Celallel, Dalii, Felioque prioris.
Cesane, Camesnes, Fesinon, Banoco secundae.
Tertia Darapri, Drisamis, Darisi, Ferapro,
Bocaro, Ferisor habet. Quanta insuper addit
Bamatip, Cametes, Dimatis, Fesapto, Fesistot.
Professor Mackenzie suggests that, if this plan is adopted, it would be better to take r for the first figure (figura recta, the straightforward figure), n for the second figure (figura negativa), t for the third figure (figura tertia or particularis), and l for the fourth figure (figura laeva, the left-handed figure). Compare also Mrs Ladd Franklin, Studies in Logic, Johns Hopkins University, p. 40.
323 259. The direct reduction of Baroco and Bocardo.—These moods may be reduced directly to the first figure by the aid of obversion and contraposition as follows.[347]
Baroco:—
| All P is M, | |
| Some S is not M, | |
| therefore, | Some S is not P, |
is reducible to Ferio by the contraposition of the major premiss and the obversion of the minor, thus,—
| No not-M is P, | |
| Some S is not-M, | |
| therefore, | Some S is not P. |
[347] Another method is to reduce Baroco and Bocardo by the process of ἔκθεσις to other moods of figures 2 and 3, and thence to figure 1. Ueberweg writes, “Baroco may also be referred to Camestres when those (some) S of which the minor premiss is true are placed under a special notion and denoted by Sʹ. Then the conclusion must hold good universally of Sʹ, and consequently particularly of S. Aristotle calls such a procedure ἔκθεσις” (Logic, § 113). As regards Bocardo, “Aristotle remarks that this mood may be proved without apagogical procedure (reductio ad impossibile) by the ἐκθέσθαι or λαμβάνειν of that part of the middle notion which is true of the major premiss. If we denote this part by N, then we get the premisses; NeP ; NaS: from which follows (in Felapton) SoP ; which was to be proved” (§ 115). The procedure is, however, rather more complicated than appears in the above statements. In the case of Baroco (PaM, SoM, ∴ SoP), let the S’s which are not M (of which by hypothesis there are some) be denoted by X ; then we have PaM, XeM, ∴ XeP (Camestres); but XaS, and hence we have further XeP, XaS, ∴ SoP (Felapton). In the case of Bocardo (MoP, MaS, ∴ SoP), let the M’s which are not P (of which by hypothesis there are some) be denoted by N ; then we have MaS, NaM, ∴ NaS (Barbara); and hence NeP, NaS, ∴ SoP (Felapton). The argument in both cases suggests questions connected with the existential import of propositions; but the consideration of such questions must for the present be deferred.