Universa Philosophia

We use syllogisms in many ways, in which three terms are found, which are the subject and predicate. Of these one is repeated in each premise, and is left unsaid in the conclusion; this is called the middle term. The other two terms are posited, one in the major premise, which is called the major extreme: the other is posited in the minor, and is called the minor extreme: but these two are repeated in the conclusion. The figure is taken from the way in which the middle term is subjected or predicated in each premise.

For, in the first place, the middle term can be the subject in the major and the predicate in the minor, which is called the first figure. For example, every man runs, Peter is a man: therefore Peter runs: this is the first figure. The second figure is that in which the middle term is the predicate in each premise, for example, no man is a brute, every lion is a brute: therefore no lion is a man. The third figure is that in which the middle term is the subject of each premise, for example, no man is a stone, every man is risible: therefore no risible thing is a stone. Galen added a fourth figure, in which the middle term is the predicate in the major and the subject in the minor. This differs from the first figure only because the premises are posited in inverted order. For example, if you say, every man runs, Peter is a man: therefore Peter runs, this syllogism is in the first figure; but if you place the minor in the first place and the major in the second, you will make the fourth figure, for example, Peter is a man, but every man runs: therefore Peter runs. Behold, by the mere transposition of the premises, without addition or subtraction of a word, the fourth figure is made: but because this transposition is of little moment, therefore it is not distinguished from the first.

The mode is that by which syllogisms are posited as affirmative or negative, particular or universal. These modes are contained in these four verses.

Barbara, celarent, darii, ferio, baralipton
Celantes, dabitis, fapesmo, frise somorum,
Cesare, camestres, festino, baroco, darapti,
Felapton, disamis, datisi, bocardo, ferison.

I premise that the individual modes consist of three vowels, signifying the quantity and quality of the proposition; and those vowels are A. E. I. O. A. signifies a universal affirmative proposition, E. a universal negative, I. a particular affirmative, O. a particular negative. Three vowels, therefore, in their order signify the three propositions of the syllogism, for example, Barbara three universal affirmatives, Celarent the first a universal negative: the second a universal affirmative: the third a universal negative. Note that Baralipton and frise somorum consist of four vowels: but the fourth signifies nothing, but serves only for the sound of the verse.

The four modes of the first verse are of the first figure, concluding directly: because the major extreme is predicated of the minor, for example in Barbara, every man runs: every rational thing is a man: therefore every rational thing runs. Likewise in celarent. No man runs: every rational thing is a man: therefore no rational thing runs. I say the same of darii and ferio: whose examples are easy for boys. But the fifth mode of the first verse, and the four of the second, are of the same first figure, concluding indirectly: because the minor extreme in the conclusion is predicated of the major, for example in Baralipton, every man runs: every rational thing is a man: therefore some running thing is rational: this syllogism in its premises differs in nothing from Barbara: but in the conclusion it differs: because Barbara says, therefore every rational thing runs. You will find the same in the other modes, for by that account celantes differs from celarent, dabitis from darii, fapesmo and frise somorum from ferio, but with some change, as I shall say, §. 35.

To the second figure belong the four first modes of the third verse, Cesare, camestres, festino, baroco. For example in Cesare, no man runs: every brute runs: therefore no brute is a man. Camestres differs in nothing from Cesare except in the inversion of the premises: for example, every brute runs: no man runs: therefore no man is a brute. Festino is the third mode: no man runs: some lion runs: therefore some lion is not a man. Barocho: every man runs: some animal does not run: therefore some animal is not a man. I said in disputation 10 of the Logic, §. 3. that in this second figure one can conclude indirectly.

The third figure embraces the fifth mode of the third verse, and the other five of the last verse, Da-rapti, whose example is, every man runs: some man is white: therefore something white runs. Felaptom, no man runs: every man is white: therefore something white does not run: the examples of the other modes are very easy. These three figures with these modes conclude evidently, so that, both premises being conceded, the consequence cannot be denied except by a fool. But the first four modes of the first figure are so manifest that anyone who denies the consequence is to be sent away from the schools: but since we can reason in many ways in any figure whatsoever, there are in each many useless modes: in the first figure there are twelve reviewed by me in that disputation 10, §. 83. In the second figure I reviewed just as many useless ones, ibidem §. 113. but in the third there are ten useless modes, enumerated ibidem §. 119. which I pass over here for the sake of avoiding prolixity.

Observing that nothing at all follows from purely negative [premises], nor from purely particular ones, nor from four terms, nor from two, but from three so disposed that in the premises of an affirmative syllogism it is conceded that the same middle term is [identical] with each extreme: whence the conclusion infers that the extremes are the same among themselves, on account of that metaphysical principle, those things which are the same as one third thing are the same among themselves: evident indeed in created things. On this principle rests the logical principle, dici de omni, that is, when something is said of one thing, it is also said of every other thing which is really the same as that. But in a negative syllogism (such as is the one which has only one affirmative proposition, but two negative ones) it must be shown in the premises that the identity of one extreme with the middle term is denied, and that the identity of the other extreme with the same middle term is affirmed: whence is concluded the denial of the identity of the extremes among themselves. For this reason logicians speak of dici de nullo, that is, when something is denied of some thing, it is said of no thing identified with that thing. There are some other syllogisms, e. g. the one they call expository, consisting of purely singular [propositions], for example, this man is king: Anthony is this man: therefore Anthony is king. These syllogisms are the most manifest of all, whether they be affirmative or negative. A modal syllogism can also be made, and others which are very easy, which I discussed in that disputation 10, sect. 24.

In Galen's fourth figure there can be established as many modes as in the first, and concluding for the same reason, which can be called.

Barnaba, Galerent, dimari, firemo, Bamaliptom.
Calemes, dimatis, fesapo, fresisonorum.