DIVISION AND CLASSIFICA TION. 1 1 9 



divide triangles on the basis of equality of length of sides, we set 

 down two members of the division, equilateral and isosceles, and 

 then, passing to another basis, viz. size of angles, we set down as 

 a -third member, right-angled triangles : for we thus include right- 

 angled isosceles triangles twice, while excluding obtuse-angled- 

 scalene and acute-angled-scalene altogether. On the other hand, 

 a division of triangles into equiangular, isosceles, and scalene, 

 happens to be accurate, though made on a twofold basis, because 

 the two principles simultaneously, employed (relation of angles 

 and relation of sides) happen to give the same sub-classes. So, 

 too, the division of animals into cloven-footed and non-ruminants 

 happens not to be a cross-division simply because the two bases, 

 employed simultaneously, happen to coincide in their results. 

 These divisions are, nevertheless, logically unsound, because by 

 confusing different grounds in the same act of division they lead 

 to sub-classes which do not exhibit, as they should, their mutual 

 exclusiveness. 



It is sometimes stated, 1 in connexion with the rule under con 

 sideration, that we should preserve the same basis, not merely 

 throughout any single act of dividing a genus into its proximate 

 co-ordinate species, but as far as possible throughout all the subse 

 quent stages of sub-division of these species ; not, of course, the 

 same identical mode of that basis, but some variation of the latter 

 (58) : so that on the predicamental line leading from the genus 

 to any one of its inftmce species, each differentia will appear as a 

 more definite and specific mode of the preceding differentia: 

 &quot; When the division is carried further than one stage, the same 

 fundamentum divisionis should be retained in the later stages 

 which was used in the first&quot;. 2 It is certainly desirable to ex 

 haust in this way the potentialities of a given basis of division as 

 far as may be feasible : it will have the advantage of showing all 

 the sub-classes thus derived to be &quot;alternative developments of a 

 common notion, or variations on a common theme&quot; ; 3 thus trac 

 ing the generic notion downwards through its specific embodi 

 ments. It will have this advantage, too, that a differentia which 

 is a modification of a preceding one can never be predicated of 

 any other class co-ordinate with the preceding genus 4 ; whereas 



1 Cf. JOSEPH, op. cit., pp. 104, 112, 116. 

 &quot;*ibid., p. 104. Cf. supra, 49. 3 ibid. t p. 108. 



4 &quot; Biped is not applicable to footless, the other member along with footed of 

 the genus animal.&quot; JOSEPH, op. cit., p. 116. 



