692 THE PRINCIPLES OF SCIENCE. [CHAP. 



reached until at least three previous false systems had 

 been long entertained. And though there is much reason 

 to believe that the present mode of classification according 

 to atomicity is substantially correct, errors may yet be 

 discovered in the details of the grouping. 



Symbolic Statement of the Theory of Classification. 



The theory of classification can be explained in the most 

 complete and general manner, by reverting for a time to 

 the use of the Logical Alphabet, which was found to be of 

 supreme importance in Formal Logic. That form expresses 

 the necessary classification of all objects and ideas as depend- 

 ing on the laws of thought, and there is no point concerning 

 the purpose and methods of classification which may not be 

 stated precisely by the use of letter combinations, the only 

 inconvenience being the abstract form in which the subject 

 is thus represented. 



If we pay regard only to three qualities in which things 

 may resemble each other, namely, the qualities A, B, C, 

 there are according to the laws of thought eight possible 

 classes of objects, shown in the fourth column of the 

 Logical Alphabet (p. 94). If there exist objects belonging 

 to all these eight classes, it follows that the qualities A, B, 

 C, are subject to no conditions except the primary laws of 

 thought and things (p. 5). There is then no special law of 

 nature to discover, and, if we arrange the objects in any 

 one order rather than another, it must be for the purpose of 

 showing that the combinations are logically complete. 



Suppose, however, that there are but four kinds of objects 

 possessing the qualities A, B, C, and that these kinds are 

 represented by the combinations ABC, AJC, aBc, abc. 

 The order of arrangement will now be of importance ; for if 

 we place them in the order 



r ABC f A5C 



( aBc ( abc 



placing the B's first and those which are b's last, we shall 

 perhaps overlook the law of correlation of properties in- 

 volved. But if we arrange the combinations as follows 

 ( ABC ( aBc 



\ A&C { abc 



it becomes apparent at once that where A is, and only 

 where A is, the property C is to be found, B being 



