114 REASONING. 



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 ipossihle 7?iode, 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 di%Tiiing 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 peculiar perspicuity, the 

 whole of the common docti'ine of the syllogism. 



' AH valid ratiocination ; all reasoning by which, from general propo- 

 sitions previously admitted, other propositions equally or less general 

 are infeiTed ; 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, regidar in mode and figure. 



• Although a syllogism framed according to any of these formulffi is a 

 valid argument, all correct ratiocination admits of being, stated in syllo- 

 gisms of the first figure alone. The rules for throwing an argument in 

 any of the other figures into the first figiire, are called rules for the re- 

 duction 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, 

 may be reduced as follows. The proposition. No O is B, being an uni- 

 versal negative, admits of siniple conversion, and may be changed into 

 No B is C, which, as we showed, is the veiy same assertion in other 

 words — the same fact differently expressed. This ti-ansformation hav- 

 ing been effected, the argument assumes the followdng fonn : — 



No B is C 



AH A is B 

 therefore 



No A is C, 

 which is a good syllogism in the second ode of the first figure. Again, 

 an argument in the first mode of the third figure must resemble the 

 following : — 



All B is C 



All B is A 

 therefore 



Some A is C, 

 where the minor premiss. All B is A, conformably to what was laid 

 dawn in the last chapter respecting universal afflnnatives, does not ad- 

 mit of simple conversion, but may be converted ^er accidens, thus; Some 



