Each figure is divided into _modes_, 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 modes, that is, all those in which the conclusion correctly follows from the premisses. A is the minor term, C the major, B the middleterm.
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
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
All B is C No B is C Some B is C All B is C Some B is No B is C not C All B is A All B is A All B is A Some B is A All B is A Some B is A therefore therefore therefore therefore therefore therefore Some A is C Some A is Some A is C Some A is C Some A is Some A is not C not C not C
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 of 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 mode of the first figure.
The reasons why syllogisms in any of the above forms are legitimate, that is, why, if the premisses be true, the conclusion must necessarily be so, and why this is not the case in any other possible _mode_, (that is, in any other combination of universal and particular, affirmative and negative propositions,) any person taking interest in these inquiries may be presumed to have either learnt from the common school books of the syllogistic logic, or to be capable of divining for himself. The reader may, however, be referred, for every needful explanation, to Archbishop Whately's _Elements of Logic_, where he will find stated with philosophical precision, and explained with remarkable perspicuity, the whole of the common doctrine of the syllogism.