286 THE SCIENCE OF LOGIC 



or V&quot; would have exactly the same meaning as &quot; Either X or Y&quot;. 

 &quot; Anyone who acts thus is either dishonest or unwise &quot; would 

 mean exactly the same as &quot; Anyone who acts thus is either honest 

 or wise &quot;. 



The exclusive interpretation of the alternative proposition is 

 advocated by some logicians on the ground that the function of 

 the judgment with alternative predicates is to express the results 

 of a logical division or classification : that, therefore, the alterna 

 tive predicates, which give the sub-classes within the logical whole 

 or system, should, according to the rules of logical division, be 

 mutually exclusive, and at the same time collectively exhaustive of 

 the denotation of the subject-term (62). Hence, they say, the 

 ideally perfect alternative proposition should fulfil these con 

 ditions. No doubt, the alternative proposition can be made to 

 fulfil this function, and, in so far as it does, it must verify the 

 conditions referred to. But the fact remains that the alternative 

 proposition is not limited to, or even used primarily for, this 

 purpose, but is used to express alternatives independently of 

 logical division. And so long as it is used in this latter way 

 it must be interpreted in the non-exclusive sense. 



Of course, z/ we assume that the alternative predicates of such judgments 

 always give us what we can make out to be co-ordinate sub-classes under 

 the genus indicated by the subject term, then indeed the alternatives must 

 always not merely differ somehow from one another but be exclusive of one 

 another and incompatible with one another. But they are not always 

 mutually exclusive, co-ordinate classes ; though they must always differ 

 somehow from one another : else the alternatives &quot; would merge into one &quot;.* 

 But difference is not exclusion or incompatibility. When we say of a 

 &quot; candidate &quot; that he must be &quot; either a graduate of the Queen s or of the 

 National, etc.,&quot; we assert that he must have the common or generic attribute 

 of &quot; graduateship &quot; in which all these alternatives agree ; we see, too, that the 

 alternatives differ as to &quot; place of graduation &quot; ; but we see at the same time 

 that the candidate may combine in himself a number of these &quot; differences &quot; 

 that they are not mutually exclusive differences. Hence it is scarcely 

 accurate to say that the points in which such attributes differ from one 

 another are &quot; points of exclusion &quot;. 2 They are not the same of course ; but 

 the same subject may possess them all, and belong simultaneously to the 

 classes denoted by each of them respectively. 



146. RELATION OF ALTERNATIVE TO HYPOTHETICAL AND 

 CATEGORICAL JUDGMENTS. OPPOSITION AND EDUCTION IN AL 

 TERNATIVE JUDGMENTS. Since every alternative proposition 



1 WELTON, Logic, i., p. 190. 2 ibid. 



