220 SCIENCE PROGRESS 



The seventh rule of the syllogism is that it is impossible to 

 draw any conclusion from premisses both of which are par- 

 ticular ; and, as already explained, by a particular premiss is 

 meant a statement about " Some," or part of a class. Nearly 

 all the arguments already given achieve this impossibility, and 

 so does the following : 



XIX. If Some of the army were infantry, 



and Some of the army were cavalry ; 



then The army consisted of at least two arms, (Affirmative.) 



and The army did not consist wholly of infantry. (Negative.) 



The eighth and last rule of the syllogism proclaims the 

 impossibility of reaching a universal conclusion (that is, a 

 conclusion about the whole of a class) if one premiss is par- 

 ticular (that is, refers to part only of a class). This impossi- 

 bility is achieved by the arguments II., III., VI., IX., XII., 

 XVII., XVIII., and XIX., so that it is unnecessary to give 

 another; but to complete the tale I offer the following 



argument : 



If Some of them are infantry, 



and Others are cavalry, 



and Others are artillery, 



and The rest are naval officers ; 



then None of them is a civilian. 



This argument breaks the first rule of the syllogism, for it 

 contains more than three propositions ; it breaks the second, 

 for it contains more than three terms ; it breaks the third rule 

 in several pieces, for it contains no middle term, and no term in 

 the premisses is distributed ; it breaks the fourth rule, for the 

 conclusion contains a term, " None of them," which is distri- 

 buted, though the term " them " is not distributed in any 

 premiss; it breaks the sixth rule, for the conclusion is nega- 

 tive, though every premiss is affirmative ; it breaks the seventh 

 rule, for it reaches a conclusion from premisses every one 

 of which is "particular" — refers to part only of a class; and 

 it breaks the eighth rule, for it reaches a universal conclusion — 

 a conclusion about the whole of a class — from premisses of which, 

 not one only, but all are particular. The only rule it does 

 not break is the fifth, which forbids us to draw a conclusion 

 from two negative premisses. Yet this argument, which is 

 in flat violation of seven out oi the eight rules of the syllo- 



