186 



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 hoth ranked in the first 

 mood of the first figure. 



The reasons why syllogisms in any of the above forms are 

 legitimate, that is, why, if the premises are true, the conclu 

 sion must inevitably be so, and why this is not the case in 

 any other possible mood, (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 learned from the common school books of the 

 syllogistic logic, or to be capable of discovering for himself. 

 The reader may, however, be referred, for every needful expla 

 nation, 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 gene 

 ral 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 

 mood and figure. 



Though a syllogism framed according to any of these for 

 mulas 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 

 premises. Thus an argument in the first mood of the second 

 figure, as 



No C is B 



All A is B 



therefore 



No A is 0, 



may be reduced as follows. The proposition, No C is B, 



