from it; add this new negative class to the supposed summum genus, and we form a still higher genus, which is absurd.
Although there is no absolute summum genus, nevertheless relatively to any branch of knowledge or any particular 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 comprehend all notions capable of numerical discrimination. The biologist, on the other hand, has a narrower sphere containing only organised 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 reasoning beings of his own country together with their property.
In the description of the Logical Alphabet it was pointed out (p. 93) that every series of combinations is really the 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.16 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