ON VARIOUS POINTS OF THE ONYMATIC SYSTEM. 475 



a spade. But the imp, while he was gone, tied a garter of exactly the same form and colour 

 over every thistle in the field. When the poor man came back, he was made sadly sensible 

 of the impossibility of distinguishing two individuals by the difference of their points of 

 agreement. Hamilton would have described the situation to him as follows (VI. 643*) : — " Let 

 us consider what is meant by the proposition, — " This thistle has a garter." " A garter" does 

 not here imply all, every, or even any garter, but some garter, — a certain garter ; and this 

 particulare, — be it vagum, be it signatum, — this some or certain garter which we affirm to be 

 on this thistle, we do deny to be on that, in denying this to be that." To which the Irishman 

 might reply ; — " True for you, your honour ! but what will I be the better of that ? Sure 

 its the signatum I'm wanting, and the vagums are of no use at all at all." And this is 

 the true answer. If we only know that the garter on this thistle is not the garter on that, by 

 (otherwise) knowing that this is not that, we have nothing that we can enunciate about 

 garters as giving knowledge of this and that. Any one who can make a formal profit of the 

 differentice of undistinguishable class-marks, may make a material profit of the cluricaune, if he 

 can catch the creature. In the mean time, he may employ himself in studying how to advise 

 the little boy who had two shillings, and was puzzled to find out which he ought to spend 

 first, to make his money go farthest. 



I hold this distinction between " Every man is in the class animal " and " Every man 

 is an object in which inheres one quality animal" to be of small meaning and no use. To 

 make it the great distinction between the two sides of logic seems to me solemn trifling: 

 to symbolize it by the inversion of phrase in " Some animal is all man " and " All man is 

 some animal " is to bring distinction without difference in aid of difference without distinction. 



In my third paper I gave a generalization of the old distinction of extension and compre- 

 hension (or intension) as the foundation of what I called the mathematical and metaphysical 

 sides of logic. To all there laid down I adhere ; but I add that the logical skeleton of the 

 metaphysical side is connected with whole in relation to part just in the same manner as that 

 of the mathematical side is connected with part in relation to whole. Every attribute, or 

 concept by which a class is distinguished, makes many portions of the universe to be so many 

 wholes in relation to contained parts. If the class X be a part of the class Y, the class 

 Y is a whole of the class X, the attribute Y is a component of the attribute X, whenever we 

 mean by the attribute X the total attribute, the compound of all possible attributes, possessed 

 by X. The proposition is 'X and every part of X' — not merely its distinct parts, but all 

 possible parts — comes under Y and all its wholes. The correlation of part and whole 

 has been so little examined that further detail may be necessary. 



There are classes, X and Y, containing 20 and 30 individuals: they aggregate into a class 

 of not less than 30 nor more than 50 individuals; and I must know how many individuals 

 belong to both classes before I can assign the aggregate number ; that is, before I can 

 ascertain the common whole of which X and Y are parts I must know the common part, if 

 any, of which X and Y are wholes: this common part may be of any number of individuals 

 not exceeding 20. This is the principle which Mr Boole has formulised in X+Y-XY for 

 the aggregate of X and Y; and which determined my use of (X, Y) instead of X + Y in 

 my Formal Logic. I call the common whole of two parts their aggregate; the common 

 part of two wholes their compound. 



