DIVISION AND CLA SSI PICA TION. 1 1 3 



Or, again, we may take as fundamentum divisionis for triangles 

 the size of the largest angle, thus also arriving at three sub-classes : 

 obtuse-angled, having one angle of more than ninety degrees ; 

 right-angled, having one angle of ninety degrees ; and acute- 

 angled having each angle less than ninety degrees. 1 From the 

 latter example it will be seen that the same genus can be divided 

 in various ways according as we take different grounds of division. 

 Such distinct processes of dividing the same genus are termed 

 co-divisions; each yields sub-classes which may partially or 

 totally overlap those of the others. The sub-classes yielded by 

 any one act of division are called co-ordinate species of the genus 

 divided. Each of these sub-classes may be itself logically divided 

 on some new 2 basis, into two or more narrower classes, and these 

 again on another basis into other still narrower groups, and so 

 on. This continued application of the process is called sub 

 division. It may be carried from a summum genus right through 

 any predicamental line down to the infima species which has only 

 individuals under it,,(46). 



59. RELATION TO DEFINITION AND KINDRED PROCESSES. 

 Just as definition serves to introduce distinctness into our ideas by 

 setting forth their connotation, so division introduces clearnessby 

 marking the boundaries of their denotation (49). The two pro 

 cesses are complementary and inseparable from each other. We 

 define a species by assigning its proximate genus and its specific 

 difference. The latter becomes a fundamentum divisionis for the 

 genus and suggests the division of the latter into the species de 

 fined and one or more co-ordinate species. The essential function 

 of both processes is to trace out the different embodiments or 

 realizations of our generic concepts in the things of experience. 

 And while their combined application enables us to arrange, 

 compare, co-ordinate, and subordinate, our general concepts of 



1 In each of these examples we can see from the very nature of the genus in 

 question that there can be no other alternative modes or species of it besides those 

 enumerated; we divide the genus &quot;with a perception that the species revealed in 

 experience are such as must necessarily have existed in that genus&quot; (JOSEPH, op. 

 cit., p. 119). But this is owing to the peculiar clearness of the abstract intuitions of 

 space with which geometry deals. In the concrete, physical sciences, we have no 

 such a priori conviction that the divisions we make must be exhaustive. Here we 

 must wait on experience for an a posteriori verification of our classifications (62). 



* i.e. new in the sense that it cannot be a mere repetition of the previous basis, 

 but must be a special modification of the latter, or another and distinct modifica 

 tion of the genus as already specified by the previous basis. Cf. supra, 43 ; infra, 

 62; JOSEPH, op. cit., pp. 112, 116 sqq. 



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