3S 8 THE SCIENCE OF LOGIC 



any act is done from purely selfish motives, it is always formally 

 wrong ; therefore, if any act is done from purely selfish motives, 

 it is not done from a sense of duty.&quot; l 



The following example of Bocardo in the third figure, taken 

 from the same context, illustrates the function of the problematic 

 or particular hypothetical as denying that something is necessarily 

 connected with something else : &quot;If [though] a war is \be\ just it is 

 sometimes not [or need not be\ successful ; if any war is just it 

 is always waged in defence of some right; therefore, if a war is 

 [though a war be\ waged in defence of some right, it is sometimes 

 not [or need not necessarily be] successful &quot;. 2 



All the other moods and figures of the pure hypothetical 

 syllogism may be reduced to the moods of the first figure by 

 applying the ordinary rules for reduction. Baroco and Bocardo 

 may be reduced directly to Ferio and Darii respectively, by follow 

 ing the rules of the mnemonics Faksoko and Doksamosk. Thus, 

 the example of Bocardo given above may be reduced to Darii 

 by contraposing (ks) the original major, transposing (;) the 

 premisses, and finding the obverted converse (sk} of the new con 

 clusion. 



If any war is just it is always waged in defence of some 

 right ; 



Though a war be unsuccessful it is sometimes just ; 



Therefore, Though a war be unsuccessful it is sometimes waged 

 in defence of some right ; 



Therefore, Though a war be waged in defence of some right it 

 is sometimes unsuccessful ; 



Therefore (original conclusion), Though a war be waged in 

 defence of some right it is sometimes not successful. 



175. THE MIXED HYPOTHETICAL SYLLOGISM. The mixed 

 hypothetical, or hypothetico-categorical, syllogism, is a syllogism in 

 which the major premiss is a hypothetical or a conditional pro- 

 position, the minor premiss categorically posits the antecedent 

 or sublates the consequent of the major, and the conclusion ac 

 cordingly posits the consequent or sublates the antecedent of the 

 major. There is no need to distinguish here between \hzpure or 

 abstract hypothetical, and the concrete conditional, premiss (133); for 

 the basis of the reasoning involved is the same in both cases. By 

 stating the major premiss in the conditional or denotative form, the 

 syllogistic character of the inference as being the application, to 

 1 ibid. 3 ibid. 



