12 1. 3. 



Again, if the species are ultimate indivisible groups, that is, 

 are groups with indivisible differentiae, and if no differentia be 

 common to several groups, the number of differentiae must be 

 equal to the number of species. If a differentia though not 

 divisible could yet be common to several groups, then it is 

 plain that in virtue of that common differentia specifically dis- 

 tinct animals would fall into the same division. It is necessary 

 then that none of the differentiae that belong to the ultimate or 

 indivisible groups shall be common ; for otherwise, as already 

 said, specifically distinct animals will come into one and the 

 same division. But this would violate one of the requisite 

 conditions, which are as follows. No ultimate group must be 

 included in more than a single division ; different groups must 

 not be included in the same division ; and every group must be 

 found in some division. It is plain then that we cannot get at 

 the ultimate specific forms of the animal, or any other, kingdom 

 by bifurcate division. If we could, the number of ultimate 

 differentiae would equal the number of ultimate animal forms, 

 [which is inconceivable]. For assume an order of beings whose 

 prime differentiae are White and Black, Each of these branches 

 will bifurcate, and their branches again, and so on till we reach 

 the ultimate differentiae, whose number will be four or some 

 other multiple of two, and will also be the number of the 

 ultimate species comprehended in the order. 



(A species is constituted by the combination of differentia and 

 matter. For no animal, nor portion of an animal, is purely 

 material or purely immaterial, in other words purely corporeal or 

 purely incorporeal, as repeatedly observed.) 



Further the differentiae must be elements of the essence, and 

 not merely properties or attributes. Thus if Figure is the 

 term to be divided, it must not be divided into figures whose 

 angles are equal to two right angles, and figures whose angles 

 are together greater than two right angles. For it is only an 

 attribute of a triangle and not part of its essence that its angles 

 are equal to two right angles. 



Again the bifurcations must be contradictories, like White and 

 Black, Straight and Bent ; and if we characterize one branch by 

 either term, we must characterize the other by its opposite, and 

 not, for example, characterize one branch by a colour, the other 

 by a mode of progression, swimming for instance. 

 643 a. 



