120 THE SCIENCE OF LOGIC. 



when a &quot; new &quot; basis is introduced into a scheme of division, it 

 may, for all we know, be predicable of some other class, co-ordin 

 ate with some higher genus. 1 Aristotle seems to have regarded 

 the former as the more proper sort of division (tcara TO opBov), 

 counting all the subordinate differentiae between the genus and 

 its infima species as one ; and to have regarded any division which 

 separated the infima species from the genus by a number of dis 

 tinct differentiae, unrelated to one another so far as our knowledge 

 goes (67), as less proper and less scientific (/cara TO a-v/jL/Se^rjKosi)- 2 

 But this method of division is not always possible in dividing 

 the summa genera of things in the world around us into sub 

 classes, or in grouping together (or classifying) species into genera. 

 We are forced repeatedly by facts to recognize, between sub 

 classes of things, differentiae which we cannot see to be modifica 

 tions of, or in any necessary way connected with, the higher 

 differentiae of the higher genera to which these sub-classes belong. 

 In all such cases, what we may call the total basis on which the 

 genus is differentiated into an infima species is the combina 

 tion of all the various differentiating concepts employed. Thus, 

 Aristotle based his division of matter into four fundamental 

 elements on the combination of two attributes, temperature and 

 humidity : 



Matter 

 I 



RULE II. This rule may be violated in two ways : by omit 

 ting some of the sub-classes, or by including some that are not 

 sub-classes, of the genus : in other words, by making the division 

 too narrow or too wide. In either case it is not the supposed 

 genus that is divided, but that genus plus or minus some additional 

 group or groups of objects. We are not likely to violate these 

 rules in simple cases : to divide triangles into equilateral and 

 isosceles, omitting scalene ; or to divide coins into gold, silver, 

 copper, and banknotes. But the accurate logical division of the 



1 &quot;Feathered and featherless might be applicable to quadruped no less than to 

 biped &quot; (ibid.) ; rational might be predicable not only of man but of incorporeal 

 substances such as angels (cf. p. 73 . 3). 



*ibid., p. 116. 



