ON VARIOUS POINTS OF THE ONYMATIC SYSTEM. 



437 



Hamilton arranges these under twelve heads. Each head has three syllogisms : one with 

 both premises affirmative ; two others formed by making one premise negative without altera- 

 tion of quantities. Thus ) ( ) ) is accompanied by ) • ( ) ) and )()•), as follows : 



) ( ) ) All X is all Y and All Y is some Z. 

 ) • ( ) ) Any X is not any Y and All Y is some Z. 

 ) ( )•) All X is all Y and Any Y is not some Z. 



The negative syllogisms take the number of the positive one from which they are derived, 

 with the letters a and b. The canon of inference may be stated as follows : — When one 

 premise is ) ( the form of the other is that of the conclusion : in every other case the erasure 

 of the two middle spiculse shows the form of the conclusion. I now make a table, adding a 

 word of necessary remark in certain cases. 



I 

 II 



III 

 IV 



V 



VI 



VII 



VIII 



IX 



X 

 XI 

 XII 



)()( 

 (()) 

 )()) 

 {()( 

 )((( 

 )))( 

 ((() 

 ())) 

 )(() 

 ())( 

 (((( 

 )))) 



Of 36 syllogisms, 21 have no error either of commission or omission : which arises as 

 follows. Those marked (*), 15 in number, are safe because they contain ) (, the sign of 

 equivalence. Let the other signs have any degree of absurdity, or even of contradiction, 

 any one of them joined with ) ( only means that one of the terms is to be extracted, and an 

 equivalent inserted in its place: consequently X ) ( Y (•( Z, for example, must give X (-(Z, 

 let (•( mean what it may. Two others, marked (f), contain and conclude with the vague 

 form (•), which " quadrates with all the rest"; and their principle is that some (when singly 

 partitive) of the part is an equivalent of some of the whole. Remember that Hamilton did not 

 intrude double partition into the meaning of (•). Four more, marked (J), involve "some" 

 only in one term of a universal affirmative, in which double partition is of the same effect as 

 single. All the rest — being precisely all those which give working effect to the peculiar 

 diffierentice of Hamilton's system, — are either false or incomplete: eleven false, four incom- 

 plete. [I proved this in detail, in due compliment to the reputation of the proposer : but I 

 omit' the proofs, because I find that the point is not to be contested. December 1862.J 



' In the AtheruEum journal I took for my instance a case of I all lawyer; any lawyer is not any stone; therefore some man 

 IV. b, which I called the Gorgon syllogism. " Some man is I (i.e. lawyer) is not any stone (i.e. all the rest are stone)." 



