56 THE SCIENCE OF LOGIC. 



the extension increases. As a general rule, therefore, the less a 

 name implies the wider the group of things to which it applies. 



But this inverse variation is, of course, not to betaken in the 

 mathematical sense of numerical variation in the proportion of 

 two quantities. For, in the first place, we cannot measure mathe 

 matically the intension of a concept, though we may speak of 

 restricting or enlarging it. In the second place, even did we try to 

 enumerate exactly ^as so many distinct and individual entities 

 what we are pleased to call the &quot; attributes&quot; that constitute inten 

 sion, we should not necessarily in every such case interfere with the 

 denotation by the addition or subtraction of an attribute or attri 

 butes to or from the connotation. For instance, we do not lessen 

 the denotation of u man &quot; by increasing the connotation to 

 &quot; mortal man,&quot; nor do we increase the denotation of &quot; cloven- 

 hoofed ruminant &quot; by dropping from the connotation the attribute 

 &quot; cloven-hoofed &quot; ; for these attributes are common to all the 

 members of the classes in question. And in the third place, even 

 when the addition or subtraction of attributes which are not com 

 mon to the whole class does change the denotation of the original 

 concept, this change is much greater in the case of some attributes 

 than in the case of others. For instance, by adding to &quot; man &quot; 

 the attribute &quot;white,&quot; we diminish the denotation considerably; 

 but by adding instead the attribute &quot; red-haired,&quot; we diminish it 

 much more. 



What is true therefore is this, that if connotation be increased 

 or diminished, denotation will either remain unaltered or will change 

 in the opposite direction. 



Similarly, if the denotation of a given class be arbitrarily in 

 creased by annexing to it another class whose members do not 

 possess all the attributes essential for membership of the first class, 

 the connotation of the concept of the larger class thus formed will 

 be necessarily smaller the number of common attributes fewer 

 than in the concept of the original class. If to the class of 

 horses we add the class of apple-trees, the concept of the new class 

 (living organisms), of which horses and apple-trees are alike 

 members, will be much poorer in connotation than that of either of 

 the original classes : for, to say an object is a living organism is to 

 convey much less information about it than to say that it is a 

 horse, or an apple-tree, as the case may be. 



Of couise the relation between a class and its sub-classes (a genus and its 

 species] is not exactly the same as that between a class and the sum-total of 



