DIVISION AND CLASSIFICATION. 127 



seen to have the richest known stock of common attributes, and 

 this already implies the best possible contribution to our know 

 ledge of the objects so classified. 1 But to determine beforehand, 

 when still face to face with the undivided summum genus, what 

 attribute is the &quot; most important,&quot; in the sense of involving the 

 greatest number of distinct and dependent modalities within it 

 (62, R. I.), and to proceed to divide on this basis is not by any 

 means an easy undertaking. Attributes of objects are not numeri 

 cally distinct entities that may be weighed, measured, and counted 

 mathematically. Nor does the real importance of an attribute 

 depend on the &quot; number &quot; of other attributes involved in it ; for 

 the &quot; number &quot; of attributes we may discern in any object depends 

 largely on the depth of our own mental analysis of that object, 

 on the number of distinct points of view from which we regard 

 it. And while some of these attributes may open up rich and 

 fruitful vistas of knowledge, others may not carry us a single step 

 beyond themselves. Considerations, therefore, of mere number 

 are useless here. Again, then, how are we to know what attri 

 butes are &quot; most important &quot; in view of general knowledge, in 

 order to base our classification on these ? 



(&) John Stuart Mill s answer is instructive. They are, he 

 says, &quot; those which contribute most, either by themselves or by 

 their effects, to render the things [in any class] like one another, 

 and unlike other things [of other classes] ; which give to the class 

 composed of them the most marked individuality ; which fill as 

 it were the largest space in their existence, and would most im 

 press the attention of a spectator who knew all their properties but 

 was not specially interested in any V 2 



The concluding words of the extract just quoted show clearly what Mill 

 means by the &quot; most important &quot; attributes ; but, unfortunately, since we can 

 never say of any objects that we know &quot; all their properties,&quot; we can never 

 be certain that the attributes which &quot; most impress our attention &quot; are really 

 the &quot; most important &quot;. The words also show, however, that the more we 

 do know about the properties of the objects to be classified, the more likely 

 we are to make a good general or natural classification provided we are &quot; not 

 specially interested,&quot; or biassed, in respect of any of these properties or any 

 special interpretation of them : a condition which, as we shall see presently 



1 And the recognition of a stock of common attributes is simply the recognition 

 of identity amid diversity, i.e. of real resemblances -thus ultimately resting on the 

 &quot; resemblance&quot; test given below. 



3 MILL, Logic, Bk. iv., chap, vii., 2, apud WELTON, op. cit., p. 142 (italics 

 ours). 



