Page:System of Logic.djvu/133

 the middle term is the subject of the major premise and the predicate of the minor. This is reckoned as the first figure. When the middle term is the predicate in both premises, the syllogism belongs to the second figure; when it is the subject in both, to the third. In the fourth figure the middle term is the subject of the minor premise and the predicate of the major. Those writers who reckon no more than three figures, include this case in the first.

Each figure is divided into moods, according to what are called the quantity and quality of the propositions, that is, according as they are universal or particular, affirmative or negative. The following are examples of all the legitimate moods, that is, all those in which the conclusion correctly follows from the premises. A is the minor term, C the major, B the middle term.

FIRST FIGURE.

All B is C  No B is C    All B is C    No B is C All A is B   All A is B   Some A is B   Some A is B therefore    therefore    therefore     therefore All A is C  No A is C    Some A is C   Some A is not C

SECOND FIGURE.

No C is B   All C is B   No C is B         All C is B All A is B   No A is B    Some A is B       Some A is not B therefore    therefore    therefore         therefore No A is C   No A is C    Some A is not C   Some A is not C

THIRD FIGURE.

All B is   No B is C   Some B is   All B is    Some B is   No B is C C                       C           C           not C All B is    All B is    All B is    Some B is   All B is    Some B is A           A           A           A           A           A therefore   therefore   therefore   therefore   therefore   therefore Some A is  Some A is   Some A is   Some A is   Some A is   Some A is C           not C       C           C           not C       not C

FOURTH FIGURE.

All C is B   All C is B   Some C is B   No C is B    No C is B All B is A    No B is A    All B is A    All B is A   Some B is A therefore     therefore    therefore     therefore    therefore Some A is C  Some A is    Some A is C   Some A is    Some A is              not C                      not C        not C

In these exemplars, or blank forms for making syllogisms, no place is assigned to singular propositions; not, of course, because such propositions are not used in ratiocination, but because, their predicate being affirmed or denied of the whole of the subject, they are ranked, for the purposes of the syllogism, with universal propositions. Thus, these two syllogisms--

All men are mortal,    All men are mortal, All kings are men,     Socrates is a man, therefore              therefore All kings are mortal,  Socrates is mortal,

are arguments precisely similar, and are both ranked in the first mood of the first figure.(50)