AND ON LOGIC IN GENERAL. 199 



XVII. I have stated that I consider the ordinary form of the syllogism as belonging to 

 the arithmetical whole, as dealing with first intentions and objective verifications. The syl- 

 logism of each of the opposed, or rather confronted, wholes of mathematical and metaphysical 

 thought, is of second intention, and deals with the notions so called. It is in fact, combination 

 of relations : the act of mind by which we see that the A of (the B of Z), or the (A of B) 

 of Z, is thinkable under one relation. Here the compound relation, or combined relation, mav 

 be represented by AB, but by no one except a mathematician who is used to the functional 

 symbol, and to the idea of (pyj/ (tvy) in its distinction between the mode of composition of x, y, 

 and that of 0, \^. I use the word combination instead of composition, to avoid raising this 

 question, and the more readily because, until we treat of sorites, combination is of two. We 

 have seen, in the appendix to my second paper, how the logician, when he has a copula which 

 does not give his syllogism, though it be transitive and convertible, has no resource except the 

 combination of relation, thrown into a syllogism of principium and exemplum. Every thing 

 depends upon our having words descriptive of second intentions, or schetical words, which 

 shall, so far as may be, have the force we want in common usage. Four sets are wanted, for 

 terminal precision and terminal ambiguity, both in the mathematical and metaphysical views. 

 Tables of the terms which I adopt for the present, and on which I invite suggestion, are given 

 in the second part. I shall now proceed to some description and remark. 



1. Terminal ambiguity, mathematical mew. Naming the universal first, and its con- 

 trary particular second, I say that X is either species or ewient of Y ; either genus or deficient.; 

 either coexternal or copartient ; either complement or coinadequate. When class is treated as 

 a philosophical unit, we have seen that the distinction of the universal and particular propo- 

 sition is an emergence from that of assertion or denial of inclusion, or of exclusion. But it 

 consists better with the actual form of thought, as trained by existing logic, not to fashion the 

 terms upon the more philosophical basis. To make them stand on the idea of universal and 

 particular I found impracticable : I have therefore taken them upon no basis at all except the 

 aptness of the several words themselves. 



Genus and species. I use these words under terminal ambiguity : thus the species may 

 be the whole genus. They have acquired much of this force in common language, by the 

 subsidence of knowledge. In old time it was necessary that man should not be a species of 

 rational animal, but the whole genus: the earth was the only abiding place of animals. But 

 since it has come into thought that animals may possibly reside in stars and planets, it is in 

 thought that man may be no more than a species of the genus. Other planets may contain 

 organised, sentient, &c. bodies which have a thinking faculty and which name, abstract, &c. 

 but in which the whole combination is so different from our own, that we should not call the 

 compound a man. A snake's body, for instance, with a man's mind. The subsidence, or pos- 

 sible subsidence, of genus into species, and the erection of species into genus, by alteration of 

 knowledge or opinion, leave the terms very nearly indeed, if not quite, in possession of terminal 

 ambiguity. 



Exient and deficient. I have been obliged to coin the first word, of which the only fault 

 is that it is an active participle. Emergent is wanted to describe the character of results ; 

 extravagant and transcendent have their derived meanings. Deficient usually applies to that 



