DIVISION AND CLASSIFICA TION. 1 1 5 



&quot; This fault is a vice,&quot; but in reality a different logical whole is expressed in 

 these cases by the same verbal symbol as predicate. 



60. FORMAL AND MATERIAL ASPECTS OF LOGICAL DIVISION : 

 DICHOTOMY. We have already seen (50) that formal logic 

 assumes the definition or connotation of terms to be known by 

 those who make use of them, and that the treatment of definition 

 (informal logic) is justified only because, and in so far as, this 

 assumption is not verified in real life. We have now to observe 

 that without some additional knowledge of a class concept, over 

 and above what is contained in its connotation, we could never 

 subject it to the process of logical division. In order to divide 

 any genus logically, we must know some note or aspect which is 

 a separable accident of that genus, i.e. which modifies the genus 

 in a certain way as found in some, and not at all, or in a different 

 way, in other members of the genus, and which will serve, there 

 fore, as a basis QY fundamentum divisionis. And, seeing that our 

 knowledge of any such basis is not contained in what is postulated 

 by formal logic, viz. the connotation of the genus, but must 

 come from an outside source, it follows at once that the process 

 of logical division is always a partly material, never a purely 

 formal, process: unless, indeed, starting with a class A, real or 

 imaginary, we imagine an attribute B to be possessed by one, and 

 not by another, group of the class A, and on this basis divide A 

 into B and B * / and proceed similarly to divide B or B on the 

 basis of another imaginary separable accident C, into BC and 

 BC, or into BC and BC ; and so on indefinitely. Were we to 

 carry on such a process, it might indeed be Q.3\\z.& formal inasmuch 

 as it would make no appeal for information to any source in 

 dependent of the concept with which we started, and of our own 

 imagination for a basis of division ; 2 but, obviously, we should have 

 no guarantee whatever for the reality of our imagined sub-classes ; 

 their real existence would be purely hypothetical ; and in case we 

 did appeal to facts in order to check and verify our imaginary 

 divisions, these would cease to be hypothetical and formal, and 

 would become absolute and material, or real, precisely in the 

 measure in which we made that appeal. 



The division of a class, whether real or imaginary, into a pair 

 of sub-classes, the one denoted by a positive, the other by a purely 

 negative, term (39), is called Dichotomy or Division by Dichotomy. 



1 = not-B. 2 Cf. KEYNES, Formal Logic, p. 449. 



8 * 



