380 THE PRINCIPLES OF SCIENCE. 



genus, for we cannot frame the requisite notion of a class 

 forming it without implying the existence of another class 

 discriminated from it, but which with the supposed 

 summum genus will form the species of a still higher genus, 

 which is absurd. 



Although there is no absolute summum genus, neverthe- 

 less relatively to any branch of knowledge or any special 

 argument, there is always some class or notion which 

 bounds our horizon as it were. The chemist restricts his 

 view to material substances and the forces manifested in 

 them ; the mathematician extends his view so as to com- 

 prehend all notions capable of numerical discrimination. 

 The biologist, on the other hand, has a narrower sphere 

 containing only organized bodies, and of these the botanist 

 and the zoologist take parts. In other subjects there 

 may be a still narrower summum genus, as when the lawyer 

 regards only living and reasoning beings of his own 

 country. 



In the description of the Logical Abecedarium, it was 

 pointed out (vol. i. p. 108) that every series of com- 

 binations was really the development of some one single 

 class, denoted by X, which letter indeed was accord- 

 ingly placed in the first column of the table on p. 109. 

 This is the formal acknowledgment of the principle 

 clearly stated by De Morgan, that all reasoning pro- 

 ceeds within some assumed summum genus. But at 

 the same time the fact that X as a logical term must 

 have its negative x, shows that it cannot be an absolute 



summum -genus. 



There arises, again, the question whether there be any 

 such thing as an infima species, which cannot be divided 

 into any smaller species. The ancient logicians were of 

 opinion that there always was some assignable class which 

 could only be divided into individuals, but this doctrine 

 appears to me theoretically incorrect, as Mr. George 



