DIVISION AND CLASSIFICA TION. 1 1 7 



within the domain of intellectual concepts, abstracting altogether 

 from the existence or possibility of any objective counterparts for 

 those concepts. This process is known as Purely Formal Divi 

 sion. 



61. PURELY FORMAL DIVISION. The development of dicho 

 tomy along purely formal lines, i.e. through imaginary and hypo 

 thetical grounds of division, leads to the conception of the positive 

 and negative members so obtained, not as existing classes, but as 

 (possibly/^// or empty] class compartments : a conception which 

 has proved exceedingly useful and fruitful in the peculiar treat 

 ment of certain logical problems, which has come to be known 

 and described as Symbolic Logic. 



In this purely formal, dichotomous division of a given class name, the 

 number of subdivisions made will depend exclusively on the number of new 

 terms successively introduced as foundations for the successive steps. Thus, 

 taking any universe of discourse X, we may first divide it into S and S (S 

 being a shorter way of expressing not-S}; each of these, next, into M and 

 ^f ; and each of the resulting four into P end P. We have now reached 

 eight class compartments into which existing classes may be fitted. The 

 utility of this process will become apparent when we learn later on that it is 

 possible to interpret every universal proposition as denying the existence of 

 a certain class, or, in other words, as asserting the emptiness of a certain 

 compartment^ Of the eight compartments S M P, S M P, S M P, S M P, 

 S M P,&quot;S M &quot;P, S M P, S M &quot;P, the universal proposition &quot; No M is P &quot; would 

 empty the compartments containing M P, i.e., S M P and S M P ; and the 

 universal proposition &quot;All S is M &quot; would empty the compartments containing 

 S M, i.e. S M P and S M P ; the combination of both propositions thus 

 leaving S M P, S M P, S M P, S M P, as the only classes capable of existing 

 compatibly with the truth of both propositions. 1 



Were the divisions thus obtained supposed to represent existing classes, 

 and not merely class compartments, the process would be misleading and 

 invalid ; for, not every combination of attributes represents a class capable 

 of existing, e.g. the combination &quot; right-angled-equilateral-triangles &quot; re 

 presents an impossible class, an empty compartment. 



In contrast with this purely formal process, the develop 

 ment of logical division on the basis of attributes found in really 

 existing things, e.g. along real or material lines, is known as 

 Classification. Before dealing further with this latter, it will be 

 convenient to formulate certain conditions to which all logical 

 division must conform, and which are commonly known as the 

 Rules of Logical Division. 



1 C/. WELTON, Logic, i., p. 133. 



