702 THE PRINCIPLES OF SCIENCE. [CHAP. 



development of a single class, denoted by X, which letter 

 was accordingly placed in the first column of the table on 

 p. 94. This is the formal acknowledgment of the principle 

 clearly stated by De Morgan, that all reasoning proceeds 

 within an 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 minor 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 be theoretically incorrect, as Mr. George Bentham 

 long ago stated. 1 We may put an arbitrary limit to the 

 subdivision of our classes at any point convenient to our 

 purpose. The crystallographer would not generally treat 

 as different species crystalline forms which differ only 

 in the degree of development of the faces. The naturalist 

 overlooks innumerable slight differences between animals 

 which he refers to the same species. But in a strictly 

 logical point of view classification might be carried on as 

 long as there is a difference, however minute, between 

 two objects, and we might thus go on until we arrive at 

 individual objects which are numerically distinct in the 

 logical sense attributed to that expression in the chapter 

 upon Number. Either, then, we must call the individual 

 the infima species or allow that there is no such thing at all. 



The Tree of Porphyry. 



Both Aristotle and Plato were acquainted with the value 

 of bifurcate classification, which they occasionally employed 

 in an explicit manner. It is impossible too that Aristotle 

 should state the laws of thought, and employ the predicables 

 without implicitly recognising the logical necessity of that 

 method. It is, however, in Porphyry's remarkable and in 

 many respects excellent Introduction to the Categories of 

 Aristotle that we find the most distinct account of it. 

 Porphyry not only fully and accurately describes the 

 Predicables, but incidentally introduces an example for 



1 Outline of a New System of Logic, 1827, p. 117. 



