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 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 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. All valid ratiocination; all reasoning by which, from general propositions previously admitted, other propositions equally or less general are inferred; may be exhibited in some of the above forms. The whole of Euclid, for example, might be thrown without difficulty into a series of syllogisms, regular in mode and figure. Although a syllogism framed according to any of these formulæ is a valid argument, all correct ratiocination admits of being stated in syllogisms of the first figure alone. The rules for throwing an argument in any of the other figures into the first figure, are called rules for the _reduction_ of syllogisms. It is done by the _conversion_ of one or other, or both, of the premisses. Thus an argument in the first mode of the second figure, as— No C is B All A is B therefore No A is C,