308 THE SCIENCE OF LOGIC 



there would be no common element in the comparisons, no real 

 connecting link between the extremes. To make the inference 

 possible, M must be identical with P and identical with 5 ; to make 

 the inference needful, this identity must be combined with diver 

 sity diversity of aspect in M as a connecting link between two 

 diverse concepts, S and P. 



The reason why the latter terms, S and P, must be unam 

 biguous, is no less obvious : it is only about the same S as oc 

 curred in the premisses that the predication can be made and 

 only the same predication in the conclusion. 



B (3). The violation of this first rule of quantity is called the 

 Fallacy of Undistributed Middle. The middle term must be 

 distributed, i.e. taken universally, in its whole denotation, at least 

 once in the premisses : for this simple reason, that were it undis 

 tributed, i.e. taken indefinitely, in both premisses, we could not 

 be sure that the two extremes, 5 and P, were being compared 

 with the same portion of the extension of M. S might be com 

 pared with one portion, and P with another portion, of the 

 indefinite &quot;some M&quot;. And, of course, we could draw no con 

 clusion about the relation between 5 and P unless we were sure 

 of having compared each of these with exactly the same M s. 

 In order to secure this it is sufficient to have &quot; all M&quot; compared 

 with either extreme; for the &quot;all M&quot; will overlap the &quot;some, 

 possibly all M&quot; compared with the other extreme, and will thus 

 secure an identical point of reference for both extremes. 



Thus, from the premisses &quot; Some M*s are P &quot; and &quot; Some M s 

 are S&quot; : &quot; Some artisans are married&quot; and &quot;Some artisans are 

 drunkards&quot;: we cannot infer whether or not any &quot; S s are P,&quot; 

 any &quot;Drunkards are married&quot; : for the M s that are P may or 

 may not be identical with those that are 5. But if either 

 premiss makes an assertion about &quot;all M , then we know that 

 5 and P co-exist as attributes in some of the NTs, and we can 

 therefore infer that &quot;Some S s are P&quot; or that &quot;Some P s 

 are S }&amp;gt; . 



If the middle term is singular there can be no ambiguity : it will be 

 necessarily the same in both premisses. If we take &quot;Most&quot; to mean at 

 least one more than half, then, from the premisses &quot; Most M s are P ; Most 

 ATs are S &quot; we may draw the conclusion that &quot; Some S is P ; for, the 

 two mast s overlap, thus yielding a common identical element with which to 

 compare S and P. 



It is not necessary that the middle term be distributed in both premisses ; 

 but if it be, the identity of reference of the extremes is made doubly secure. 



