RATIOCINATION, OR SYLLOGISM. 



Ill 



assertion in other words — the same 

 fact differently expressed. Thistrans- 

 formation having been effected, the 

 argument assumes the following 

 form ; — 



No B is C 



All A is B 



therefore 



No A is C, 



which is a good syllogism in the 

 second mood of the first figure. Again, 

 an argument in the first mood of the 

 third figxire must resemble the follow- 

 ing :— 



All B is C 



All B is A 



therefore 



Some A is C, 



where the minor premise, All B is A, 

 conformably to what was laid down 

 in the last chapter respecting universal 

 affirmatives, does not admit of simple 

 conversion, but may be converted per 

 accidens, thus, Some A is B ; which, 

 though it does not express the whole 

 of what is asserted in the proposition 

 All B is A, expresses, as was formerly 

 shown, part of it, and must therefore 

 be true if the whole is true. We have 

 then, as the result of the reduction, 

 the following syllogism in the third 

 mood of the first figure : — 



All B is C 

 Some A is B, 

 from which it obviously follows that 

 Some A is C. 



In the same manner, or in a manner 

 on which after these examples it is 

 not necessary to enlarge, every mood 

 of the second, third, and fourth figures 

 may be reduced to some one of the 

 four moods of the first In other 

 words, every conclusion which can be 

 proved in any of the last three figures, 

 may be proved in the first figure from 

 the same premises, with a slight altera- 

 tion in the mere manner of expressing 

 them. Every valid ratiocination, 

 therefore, may be stated in the first 

 figure, that is, in one of the following 

 fonoa: 



Every B is C 



All A ). ^ 



Some A i ^ ^' 



therefor© 



All A ) . ^ 

 IS C. 



isB. 



No B is C 



AHA 



Some A 



therefore 

 No A is 

 Some A is not 



C. 



Some A 



Or if more significant 83ntnbols are 

 preferred : — 



To prove an affirmative, the argu- 

 ment must admit of being stated in 

 this form : 



All animals are mortal ; 

 All men ) 



Some men > are animals ; 

 Socrates ) 



therefore 

 All men ) 

 Some men > are mortal. 

 Socrates ) 



To prove a negative, the argument 

 must be capable of being expressed 

 in this form : — 



No one who is capable of self-control 



is necessarily vicious ; 

 All negroes ) , , . ,. 



Some negroes i *''® ^^P*^^« «f ««1^- 

 Mr. A's negro S control; 



therefore 

 No negroes are ) 



Some negroes are not ( necessarily 

 Mr. A's negro is not ) ^'^'®"^- 



Though all ratiocination admits of 

 being thrown into one or the other of 

 these forms, and sometimes gains con- 

 siderably by the transformation, both 

 in clearness and in the obviousness of 

 its consequence : there are, no doubt, 

 cases in which the argument falls 

 more naturally into one of the other 

 three figures, and in which its con- 

 clusiveness is more apparent at the 

 first glance in those figures, than when 

 reduced to the first. Thus, if the 

 proposition were that pagans may be 

 virtuous, and the evidence to prove 

 it were the example of Aristides ; a 

 syllogism in the third figure, 



Aristides was virtuous, 

 Aristides was a pagan, 



therefore 

 Some pagan w«^s virtuous, 



