AND ON LOGIC IN GENERAL. 209 



XXIV. Certain relations take precedence of all others, because they are presented by the 

 notion of naming, and spring out of its purpose, if indeed they do not themselves constitute 

 the purpose. They may be called onomatic or onymatic {nominative and nominal being 

 engaged). 



The excessive importance of these relations has enabled them to drive all others out of 

 common logic, on the pretext of every other relation being expressible in terms of these: as 

 must be the case, since these relations exist wherever names exist which apply to the same 

 object. 



The onymatic relations, to which in this paper I confine myself, are those of whole and 

 part in the two aspects of containing and contained and compounded and component ; and also 

 the relations which the notion of contraries, and the notion of true and false, introduce in con- 

 nexion with them. 



Subordinate to, and necessarily compounded in, the notion of whole and part, is that of 

 more and less, in the matter of which are the incidents of quantity. But more and less is 

 only a component of whole and part, in the form of thought : and except as such component, 

 is of no logical import. Thus injusorium is no doubt a larger class than man, and no doubt 

 for reasons : but if we knew the extent of superiority, and the reasons, neither would be of 

 any logical effect, for our present purpose ; because the more and less is not that of con- 

 taining and contained, and the relation is not onymatic. 



The distinction of aggregation and composition is the most important distinction in the 

 subdivisions of logic. Our knowledge does not suffice to define it by full description : we can 

 only illustrate it. To the mathematician we may say that it has the distinctive character of 

 a+b and ab : to the chemist*, of mechanical mixture and chemical combination : to the lawyer 

 it appears in the distinction between ' And be it further enacted ' and ' provided always.' ' 



XXV. The notion of whole and part presents itself in three different ways, giving rise 

 to three logical wholes. 



Arithmetical whole. The class as an aggregate of individuals; the attribute as an 

 aggregate of qualities of individuals. This whole is objective, of first intention, enumerative 

 of individuals in process, collative of individuals in result. It numbers, whether the nume- 

 rical result be definite or vague; and always either answers the question How many? or 

 permits that question as a pertinent supplement. As in, 200 men were on board the packet. 

 Every man is animal, Some men are learned. Some men are not some men, &c. Inductive 

 verification is conducted in this whole, which is subordinated to both the other wholes, but in 

 different ways. It is the essential character of this whole that it aggregates similar things, 

 things only distinguishable as this, that, and the other, of the same name applied in first 

 intention to all separately. And so it can only be a whole of aggregation. Composition of 

 similars is unmeaning: a human human human beingf is only a human being; we cannot 

 subdivide a class by its own name. 



The two other wholes are of second intention, subjective in character, enumerative only. 



' The chemist will some day be aware of the great mis- I combination. 

 take he has made in using the sign + to denote chemical I f This is Mr Boole's equation «• = «. 



Vol. X. Paet I. 27 



