Universa Philosophia

Aristotle used another kind of deduction, which he called ad impossibile: for when a legitimate conclusion is denied, the one denying is compelled to admit two reciprocally contradictory propositions. The first four modes of the first figure do not need to be converted: because their consequence is so evident that it cannot be denied by a person in his right mind, and one who once denies the conclusion in Barbara will more easily deny it in any other mode whatsoever.

We use four words in this deduction: nesciebatis, oriebar, letare, Romanis. In these are contained four vowels. A signifying Barbara: because it is a universal affirmative syllogism. E signifying a universal negative syllogism, celarent. I signifying darii, a particular affirmative, O ferio a particular negative.

Nesciebatis signifies the five indirect modes of the first figure, to be reduced in their order to the syllogisms signified by those vowels, for example, Baraliptom signified by the first, E. to be reduced to celarent, celantes signified by the first I. to be reduced to darii, and so the other three.

Oriebar contains four vowels, signifying in their order the four modes of the second figure: Cesare is signified by O. to be deduced to ferio: Camestres, by I. to darii: festino by E. to celarent, Baracho, by A. to Barbara.

Letare Romanis contains six vowels, signifying in the same order the six modes of the third figure. Darapti signified by the first, E. to be reduced to celarent. Felaptom signified by the first A. to be reduced to Barbara. Dissamis signified by the second E. to be deduced to celarent: and so the three other modes, corresponding to Romanis. Therefore one must consider the mode, what place it holds in those verses, for example, Datisi is the fourth mode of the third figure, to which corresponds the first vowel of Romanis, thus it is considered to be reduced to ferio: because O. signifies a particular negative mode, such as is ferio.

Therefore Baralipton is reduced to celarent. For when someone denies a legitimate conclusion, the arguer must propose to him a proposition contradictory to the denied conclusion: which the defender cannot deny: because he would at the same time deny two contradictories. For example, someone denies the conclusion in Baralipton, by which it is said some running thing is a man, the arguer is bound to infer, therefore no running thing is a man: which contradicts this, some running thing is a man: therefore, retaining the contradictory of the conclusion, and positing it in the major, and retaining the major, which had been posited in Baralipton, and positing it in the minor, the contradictory of the conceded minor is inferred, by converting it per accidens. For example, every man runs, every risible thing is a man: therefore some running thing is risible, thus it is converted: no running thing is risible (which is contradictory to the conclusion) but every man runs (which was the major in Baralipton) therefore no man is risible: which contradicts this, some man is risible: but this converts per accidens this, every risible thing is a man, which had been the minor conceded in Baralipton. And so he is compelled to admit the minor, which he had conceded in Baralipton, and also the conclusion contradicting that minor in celarent.

Celantes to darii, taking the contradictory of the conclusion for the minor, and the minor for the major, the contradictory of the major converted simply is inferred: for example, no man runs, every risible being is a man, therefore no running thing is risible, and it is reduced thus, every risible being is a man (which was the minor of celantes) but some running thing is risible (which contradicts the conclusion of celantes) therefore some running thing is a man (which contradicts this) no running thing is a man, but this converts simply to this, no man runs, which was the major conceded in celantes.

Dabitis to celarent, taking the contradictory of the conclusion for the major, and the major for the minor, the contradiction of the conceded minor is inferred, and of the minor converted simply (as I said concerning Baralipton).

Fapesmo to Barbara, just as dabitis to celarent. Frise somorum, to darii, just as dabitis to celarent. Note that the five indirect modes of the fourth figure are converted by the same reason as these, with only this difference, that what is given to the major of the fourth figure is given to the minor of the first: because they differ only in the arrangement of the premises.

The four modes of the second figure are very easy to deduce: because they take the contradictory of the conclusion for the minor, with the same major they infer the contradictory of the minor. Oriebar signifies these modes. Cesare to ferio. For example, no man runs, but every brute runs: therefore no brute is a man, thus it is converted, no man runs (which is the major of cesare) but some brute is a man (which contradicts the negated conclusion in cesare) therefore some brute does not run, (which contradicts the minor conceded in cesare.)

Camestres to darii: festino to celarent, whose examples are easy: Barocho to Barbara.